From 664f508d1cdbd2da28cc9d5153469e71e3ee2f18 Mon Sep 17 00:00:00 2001
From: wsavran <35315438+wsavran@users.noreply.github.com>
Date: Thu, 10 Feb 2022 09:11:14 -0800
Subject: [PATCH 01/29] Update setup.py

---
 setup.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/setup.py b/setup.py
index ae8d3fa3..fe846815 100644
--- a/setup.py
+++ b/setup.py
@@ -26,7 +26,7 @@ def get_version():
     long_description=long_description,
     long_description_content_type='text/markdown',
     install_requires = [
-        'numpy',
+        'numpy<=1.21.5',
         'scipy',
         'pandas',
         'matplotlib',

From d13f74f0c7e44bb10f5d3758392edd8bb1e84796 Mon Sep 17 00:00:00 2001
From: khawajasim <asimkhawaja786@gmail.com>
Date: Wed, 23 Feb 2022 17:37:56 +0100
Subject: [PATCH 02/29] quadtree csv reader (#186)

* quadtree csv reader
* included depth columns in reader
* reader name change
* cartesian_grid.bounds added
* check for zero area
---
 csep/core/regions.py  | 16 +++++++++++-----
 csep/utils/readers.py | 31 ++++++++++++++++++++++++++++++-
 2 files changed, 41 insertions(+), 6 deletions(-)

diff --git a/csep/core/regions.py b/csep/core/regions.py
index 48295b40..05c69747 100644
--- a/csep/core/regions.py
+++ b/csep/core/regions.py
@@ -517,6 +517,9 @@ def __init__(self, polygons, dh, name='cartesian2d', mask=None):
         # index values of polygons array into the 2d cartesian grid, based on the midpoint.
         self.xs = xs
         self.ys = ys
+        # Bounds [origin, top_right]
+        orgs = self.origins()
+        self.bounds = numpy.column_stack((orgs, orgs + dh))
 
     def __eq__(self, other):
         return self.to_dict() == other.to_dict()
@@ -772,13 +775,16 @@ def geographical_area_from_bounds(lon1, lat1, lon2, lat2):
     Returns:
         Area of cell in Km2
     """
-    earth_radius_km = 6371.
-    R2 = earth_radius_km ** 2
-    rad_per_deg = numpy.pi / 180.0e0
+    if lon1 == lon2 or lat1 == lat2:
+        return 0
+    else:
+        earth_radius_km = 6371.
+        R2 = earth_radius_km ** 2
+        rad_per_deg = numpy.pi / 180.0e0
 
-    strip_area_steradian = 2 * numpy.pi * (1.0e0 - numpy.cos((90.0e0 - lat1) * rad_per_deg)) \
+        strip_area_steradian = 2 * numpy.pi * (1.0e0 - numpy.cos((90.0e0 - lat1) * rad_per_deg)) \
                            - 2 * numpy.pi * (1.0e0 - numpy.cos((90.0e0 - lat2) * rad_per_deg))
-    area_km2 = strip_area_steradian * R2 / (360.0 / (lon2 - lon1))
+        area_km2 = strip_area_steradian * R2 / (360.0 / (lon2 - lon1))
     return area_km2
 
 def quadtree_grid_bounds(quadk):
diff --git a/csep/utils/readers.py b/csep/utils/readers.py
index 753d57fa..b5352279 100644
--- a/csep/utils/readers.py
+++ b/csep/utils/readers.py
@@ -719,7 +719,7 @@ def _parse_datetime_to_zmap(date, time):
         out['second'] = dt.second
         return out
 
-def load_quadtree_forecast(ascii_fname):
+def quadtree_ascii_loader(ascii_fname):
     """ Load quadtree forecasted stored as ascii text file
 
         Note: This function is adapted form csep.forecasts.load_ascii
@@ -756,4 +756,33 @@ def load_quadtree_forecast(ascii_fname):
     # reshape rates into correct 2d format
     rates = data[:, -1].reshape(n_poly, n_mag_bins)
 
+    return rates, region, mws
+
+
+def quadtree_csv_loader(csv_fname):
+    """ Load quadtree forecasted stored as csv file
+
+        The format expects forecast as a comma separated file, in which first column corresponds to quadtree grid cell (quadkey).
+        The second and thrid columns indicate depth range.
+        The corresponding enteries in the respective row are forecast rates corresponding to the magnitude bins.
+        The first line of forecast is a header, and its format is listed here:
+            'Quadkey', depth_min, depth_max, Mag_0, Mag_1, Mag_2, Mag_3 , ....
+             Quadkey is a string. Rest of the values are floats.
+        For the purposes of defining region objects quadkey is used.
+
+        We assume that the starting value of magnitude bins are provided in the header.
+        Args:
+            csv_fname: file name of csep forecast in csv format
+        Returns:
+            rates, region, mws (numpy.ndarray, QuadtreeRegion2D, numpy.ndarray): rates, region, and magnitude bins needed
+                                                                                 to define QuadTree forecasts
+     """
+
+    data = numpy.genfromtxt(csv_fname, dtype='str', delimiter=',')
+    quadkeys = data[1:, 0]
+    mws = data[0, 3:]
+    rates = data[1:, 3:]
+    rates = rates.astype(float)
+    region = QuadtreeGrid2D.from_quadkeys(quadkeys, magnitudes=mws)
+
     return rates, region, mws
\ No newline at end of file

From 74106b900b1df774be0b07373cc5081d22930e18 Mon Sep 17 00:00:00 2001
From: bayonato89 <72937672+bayonato89@users.noreply.github.com>
Date: Tue, 14 Jun 2022 23:49:43 +0100
Subject: [PATCH 03/29] New plotting routines (#190)

* Added new functions that compute and plot 95% and 97.5% confidence ranges, as well as p values for CSEP consistency tests.
---
 csep/utils/plots.py | 246 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 246 insertions(+)

diff --git a/csep/utils/plots.py b/csep/utils/plots.py
index c8c20153..ca75fa0d 100644
--- a/csep/utils/plots.py
+++ b/csep/utils/plots.py
@@ -1883,3 +1883,249 @@ def add_labels_for_publication(figure, style='bssa', labelsize=16):
             ax.annotate(f'({annot})', (0.025, 1.025), xycoords='axes fraction', fontsize=labelsize)
 
     return
+    
+def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, plot_args=None, variance=None):
+    """ Plots results from CSEP1 tests following the CSEP1 convention.
+
+    Note: All of the evaluations should be from the same type of evaluation, otherwise the results will not be
+          comparable on the same figure.
+
+    Args:
+        results (list): Contains the tests results :class:`csep.core.evaluations.EvaluationResult` (see note above)
+        normalize (bool): select this if the forecast likelihood should be normalized by the observed likelihood. useful
+                          for plotting simulation based simulation tests.
+        one_sided_lower (bool): select this if the plot should be for a one sided test
+        plot_args(dict): optional argument containing a dictionary of plotting arguments, with keys as strings and items as described below
+
+    Optional plotting arguments:
+        * figsize: (:class:`list`/:class:`tuple`) - default: [6.4, 4.8]
+        * title: (:class:`str`) - default: name of the first evaluation result type
+        * title_fontsize: (:class:`float`) Fontsize of the plot title - default: 10
+        * xlabel: (:class:`str`) - default: 'X'
+        * xlabel_fontsize: (:class:`float`) - default: 10
+        * xticks_fontsize: (:class:`float`) - default: 10
+        * ylabel_fontsize: (:class:`float`) - default: 10
+        * color: (:class:`float`/:class:`None`) If None, sets it to red/green according to :func:`_get_marker_style` - default: 'black'
+        * linewidth: (:class:`float`) - default: 1.5
+        * capsize: (:class:`float`) - default: 4
+        * hbars:  (:class:`bool`)  Flag to draw horizontal bars for each model - default: True
+        * tight_layout: (:class:`bool`) Set matplotlib.figure.tight_layout to remove excess blank space in the plot - default: True
+
+    Returns:
+        ax (:class:`matplotlib.pyplot.axes` object)
+    """
+
+
+    try:
+        results = list(eval_results)
+    except TypeError:
+        results = [eval_results]
+    results.reverse()
+    # Parse plot arguments. More can be added here
+    if plot_args is None:
+        plot_args = {}
+    figsize= plot_args.get('figsize', (7,8))
+    xlabel = plot_args.get('xlabel', 'X')
+    xlabel_fontsize = plot_args.get('xlabel_fontsize', None)
+    xticks_fontsize = plot_args.get('xticks_fontsize', None)
+    ylabel_fontsize = plot_args.get('ylabel_fontsize', None)
+    color = plot_args.get('color', 'black')
+    linewidth = plot_args.get('linewidth', None)
+    capsize = plot_args.get('capsize', 4)
+    hbars = plot_args.get('hbars', True)
+    tight_layout = plot_args.get('tight_layout', True)
+    percentile = plot_args.get('percentile', 95)
+
+    fig, ax = plt.subplots(figsize=figsize)
+    xlims = []
+    
+    for index, res in enumerate(results):
+        # handle analytical distributions first, they are all in the form ['name', parameters].
+        if res.test_distribution[0] == 'poisson':
+            plow = scipy.stats.poisson.ppf((1 - percentile/100.)/2., res.test_distribution[1])
+            phigh = scipy.stats.poisson.ppf(1 - (1 - percentile/100.)/2., res.test_distribution[1])
+            observed_statistic = res.observed_statistic
+        
+        elif res.test_distribution[0] == 'negative_binomial':
+            var = variance
+            observed_statistic = res.observed_statistic
+            mean = res.test_distribution[1]
+            upsilon = 1.0 - ((var - mean) / var)
+            tau = (mean**2 /(var - mean))
+            phigh = nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
+            plow = nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
+
+        # empirical distributions
+        else:
+            if normalize:
+                test_distribution = numpy.array(res.test_distribution) - res.observed_statistic
+                observed_statistic = 0
+            else:
+                test_distribution = numpy.array(res.test_distribution)
+                observed_statistic = res.observed_statistic
+            # compute distribution depending on type of test
+            if one_sided_lower:
+                plow = numpy.percentile(test_distribution, 5)
+                phigh = numpy.percentile(test_distribution, 100)
+            else:
+                plow = numpy.percentile(test_distribution, 2.5)
+                phigh = numpy.percentile(test_distribution, 97.5)
+
+        if not numpy.isinf(observed_statistic): # Check if test result does not diverges
+            low = observed_statistic - plow
+            high = phigh - observed_statistic
+            ax.errorbar(observed_statistic, index, xerr=numpy.array([[low, high]]).T,
+                        fmt=_get_marker_style(observed_statistic, (plow, phigh), one_sided_lower),
+                        capsize=4, linewidth=linewidth, ecolor=color, markersize = 10, zorder=1)
+            # determine the limits to use
+            xlims.append((plow, phigh, observed_statistic))
+            # we want to only extent the distribution where it falls outside of it in the acceptable tail
+            if one_sided_lower:
+                if observed_statistic >= plow and phigh < observed_statistic:
+                    # draw dashed line to infinity
+                    xt = numpy.linspace(phigh, 99999, 100)
+                    yt = numpy.ones(100) * index
+                    ax.plot(xt, yt, linestyle='--', linewidth=linewidth, color=color)
+
+        else:
+            print('Observed statistic diverges for forecast %s, index %i.'
+                  ' Check for zero-valued bins within the forecast'% (res.sim_name, index))
+            ax.barh(index, 99999, left=-10000, height=1, color=['red'], alpha=0.5)
+
+
+    try:
+        ax.set_xlim(*_get_axis_limits(xlims))
+    except ValueError:
+        raise ValueError('All EvaluationResults have infinite observed_statistics')
+    ax.set_yticks(numpy.arange(len(results)))
+    ax.set_yticklabels([res.sim_name for res in results], fontsize=14)
+    ax.set_ylim([-0.5, len(results)-0.5])
+    if hbars:
+        yTickPos = ax.get_yticks()
+        if len(yTickPos) >= 2:
+            ax.barh(yTickPos, numpy.array([99999] * len(yTickPos)), left=-10000,
+                    height=(yTickPos[1] - yTickPos[0]), color=['w', 'gray'], alpha=0.2, zorder=0)
+    ax.set_xlabel(xlabel, fontsize=14)
+    ax.tick_params(axis='x', labelsize=13)
+    if tight_layout:
+        ax.figure.tight_layout()
+        fig.tight_layout()
+    return ax
+    
+
+def plot_pvalues_and_intervals(test_results, var=None):
+    
+    variance= var
+    percentile = 97.5
+    p_values = []
+    
+    if test_results[0].name == 'NBD N-Test' or test_results[0].name == 'Poisson N-Test':
+        legend_elements = [Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
+                           Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
+                           Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
+                           Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.0125', markersize=10, markeredgecolor='k'),
+                           Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.0125 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
+                           Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.025', markersize=10, markeredgecolor='k')]
+        
+        ax.legend(handles=legend_elements, loc=4, fontsize=13, edgecolor='k')
+        
+        if test_results[0].name == 'NBD N-Test':
+            
+            for i in range(len(test_results)):
+                mean = test_results[i].test_distribution[1]
+                upsilon = 1.0 - ((variance - mean) / variance)
+                tau = (mean**2 /(variance - mean))
+                phigh97 = nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
+                plow97= nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
+                low97 = test_results[i].observed_statistic - plow97
+                high97 = phigh97 - test_results[i].observed_statistic
+                ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) - i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
+                            color='slategray', alpha=1.0, zorder=0)
+                p_values.append(test_results[i].quantile[1] * 2.0) # Calculated p-values according to Meletti et al., (2021)
+                
+            if p_values[i] < 10e-5:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
+    
+            if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
+        
+            if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
+        
+            if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
+        
+            if p_values[i] >= 0.0125 and p_values[i] < 0.025:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
+    
+            if p_values[i] >= 0.025:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)
+            
+        if test_results[0].name == 'Poisson N-Test':
+            
+            for i in range(len(test_results)):
+                plow97 = scipy.stats.poisson.ppf((1 - percentile/100.)/2., test_results[i].test_distribution[1])
+                phigh97 = scipy.stats.poisson.ppf(1- (1 - percentile/100.)/2., test_results[i].test_distribution[1])
+                low97 = test_results[i].observed_statistic - plow97
+                high97 = phigh97 - test_results[i].observed_statistic
+                ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) - i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
+                            color='slategray', alpha=1.0, zorder=0)
+                p_values.append(test_results[i].quantile[1] * 2.0)
+                        
+            if p_values[i] < 10e-5:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
+    
+            if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
+        
+            if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
+        
+            if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
+        
+            if p_values[i] >= 0.0125 and p_values[i] < 0.025:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
+    
+            if p_values[i] >= 0.025:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)
+    
+    
+    else:
+        for i in range(len(test_results)):
+            plow97 = numpy.percentile(test_results[i].test_distribution, 2.5)
+            phigh97 = numpy.percentile(test_results[i].test_distribution, 100)
+            low97 = test_results[i].observed_statistic - plow97
+            high97 = phigh97 - test_results[i].observed_statistic  
+            ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) -i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
+                        color='slategray', alpha=1.0, zorder=0)
+            p_values.append(test_results[i].quantile)
+
+        if p_values[i] < 10e-5:
+            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
+    
+        if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
+        
+        if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
+        
+        if p_values[i] >= 10e-3  and p_values[i] < 0.025:
+            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
+        
+        if p_values[i] >= 0.025 and p_values[i] < 0.05:
+            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
+    
+        if p_values[i] >= 0.05:
+            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)  
+    
+        legend_elements = [Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
+                   Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
+                   Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
+                   Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
+                   Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.025 $\leq$ p < 0.05', markersize=10, markeredgecolor='k'),
+                   Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.05', markersize=10, markeredgecolor='k')]
+
+        ax.legend(handles=legend_elements, loc=4, fontsize=13, edgecolor='k') 
+    
+    return ax        

From f75861fb78282aeb3792729ba7484aedb538869b Mon Sep 17 00:00:00 2001
From: wsavran <35315438+wsavran@users.noreply.github.com>
Date: Thu, 10 Feb 2022 09:11:14 -0800
Subject: [PATCH 04/29] Update setup.py

---
 setup.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/setup.py b/setup.py
index ae8d3fa3..fe846815 100644
--- a/setup.py
+++ b/setup.py
@@ -26,7 +26,7 @@ def get_version():
     long_description=long_description,
     long_description_content_type='text/markdown',
     install_requires = [
-        'numpy',
+        'numpy<=1.21.5',
         'scipy',
         'pandas',
         'matplotlib',

From 380c7fcda72db2ddc5cae927db3125bbd3da36f9 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 07:56:26 -0700
Subject: [PATCH 05/29] unpinned numpy version for security issues

---
 requirements.txt | 2 +-
 requirements.yml | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/requirements.txt b/requirements.txt
index e5f26286..84e32a48 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,4 +1,4 @@
-numpy<=1.21.5
+numpy
 scipy
 pandas
 matplotlib
diff --git a/requirements.yml b/requirements.yml
index 75a1c52a..fee1f67b 100644
--- a/requirements.yml
+++ b/requirements.yml
@@ -4,7 +4,7 @@ channels:
   - defaults
 dependencies:
   - python>=3.7
-  - numpy<=1.21.5
+  - numpy
   - pandas
   - scipy
   - matplotlib

From 29d0733712c644b7dd7d4ff78d43428e8dba67a4 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 10:52:27 -0700
Subject: [PATCH 06/29] added docstrings to plot_pvalues_and_intervals added
 proper imports for plot_pvalues_and_intervals minor code formatting fixed
 issue incorrect percentile in plot_pvalues_and_intervals

---
 csep/utils/plots.py | 168 ++++++++++++++++++++++----------------------
 1 file changed, 85 insertions(+), 83 deletions(-)

diff --git a/csep/utils/plots.py b/csep/utils/plots.py
index ca75fa0d..3c594805 100644
--- a/csep/utils/plots.py
+++ b/csep/utils/plots.py
@@ -6,6 +6,7 @@
 
 import scipy.stats
 import matplotlib
+import matplotlib.lines
 from matplotlib import cm
 from matplotlib.collections import PatchCollection
 import matplotlib.pyplot as pyplot
@@ -1512,6 +1513,7 @@ def plot_comparison_test(results_t, results_w=None, axes=None, plot_args=None):
 
     return ax
 
+
 def plot_poisson_consistency_test(eval_results, normalize=False, one_sided_lower=False, axes=None, plot_args=None, show=False):
     """ Plots results from CSEP1 tests following the CSEP1 convention.
 
@@ -1883,7 +1885,8 @@ def add_labels_for_publication(figure, style='bssa', labelsize=16):
             ax.annotate(f'({annot})', (0.025, 1.025), xycoords='axes fraction', fontsize=labelsize)
 
     return
-    
+
+
 def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, plot_args=None, variance=None):
     """ Plots results from CSEP1 tests following the CSEP1 convention.
 
@@ -1891,7 +1894,7 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
           comparable on the same figure.
 
     Args:
-        results (list): Contains the tests results :class:`csep.core.evaluations.EvaluationResult` (see note above)
+        eval_results (list): Contains the tests results :class:`csep.core.evaluations.EvaluationResult` (see note above)
         normalize (bool): select this if the forecast likelihood should be normalized by the observed likelihood. useful
                           for plotting simulation based simulation tests.
         one_sided_lower (bool): select this if the plot should be for a one sided test
@@ -1936,7 +1939,7 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
     tight_layout = plot_args.get('tight_layout', True)
     percentile = plot_args.get('percentile', 95)
 
-    fig, ax = plt.subplots(figsize=figsize)
+    fig, ax = pyplot.subplots(figsize=figsize)
     xlims = []
     
     for index, res in enumerate(results):
@@ -1952,8 +1955,8 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
             mean = res.test_distribution[1]
             upsilon = 1.0 - ((var - mean) / var)
             tau = (mean**2 /(var - mean))
-            phigh = nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
-            plow = nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
+            phigh = scipy.stats.nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
+            plow = scipy.stats.nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
 
         # empirical distributions
         else:
@@ -2013,118 +2016,117 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
     return ax
     
 
-def plot_pvalues_and_intervals(test_results, var=None):
+def plot_pvalues_and_intervals(test_results, ax, var=None):
+    """ Plots p-values and intervals for a list of Poisson or NBD test results
+
+    Args:
+        test_results (list): list of EvaluationResults for N-test. All tests should use the same distribution
+                             (ie Poisson or NBD).
+        ax (matplotlib.axes.Axes.axis): axes to use for plot. create using matplotlib
+        var (float): variance of the NBD distribution. Must be used for NBD plots.
+
+    Returns:
+        ax (matplotlib.axes.Axes.axis): axes handle containing this plot
+
+    Raises:
+        ValueError: throws error if NBD tests are supplied without a variance
+    """
     
-    variance= var
+    variance = var
     percentile = 97.5
     p_values = []
-    
+
+    # Differentiate between N-tests and other consistency tests
     if test_results[0].name == 'NBD N-Test' or test_results[0].name == 'Poisson N-Test':
-        legend_elements = [Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.0125', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.0125 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.025', markersize=10, markeredgecolor='k')]
-        
+        legend_elements = [matplotlib.lines.Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.0125', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.0125 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.025', markersize=10, markeredgecolor='k')]
         ax.legend(handles=legend_elements, loc=4, fontsize=13, edgecolor='k')
-        
+        # Act on Negative binomial tests
         if test_results[0].name == 'NBD N-Test':
-            
+            if var is None:
+                raise ValueError("var must not be None if N-tests use the NBD distribution.")
+
             for i in range(len(test_results)):
                 mean = test_results[i].test_distribution[1]
                 upsilon = 1.0 - ((variance - mean) / variance)
                 tau = (mean**2 /(variance - mean))
-                phigh97 = nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
-                plow97= nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
+                phigh97 = scipy.stats.nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
+                plow97 = scipy.stats.nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
                 low97 = test_results[i].observed_statistic - plow97
                 high97 = phigh97 - test_results[i].observed_statistic
                 ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) - i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
                             color='slategray', alpha=1.0, zorder=0)
                 p_values.append(test_results[i].quantile[1] * 2.0) # Calculated p-values according to Meletti et al., (2021)
                 
-            if p_values[i] < 10e-5:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
-    
-            if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 0.0125 and p_values[i] < 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
-    
-            if p_values[i] >= 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)
-            
+                if p_values[i] < 10e-5:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='red', markersize=8, zorder=2)
+                if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='#FF7F50', markersize=8, zorder=2)
+                if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='gold', markersize=8, zorder=2)
+                if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='white', markersize=8, zorder=2)
+                if p_values[i] >= 0.0125 and p_values[i] < 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='skyblue', markersize=8, zorder=2)
+                if p_values[i] >= 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='blue', markersize=8, zorder=2)
+        # Act on Poisson N-test
         if test_results[0].name == 'Poisson N-Test':
-            
             for i in range(len(test_results)):
                 plow97 = scipy.stats.poisson.ppf((1 - percentile/100.)/2., test_results[i].test_distribution[1])
-                phigh97 = scipy.stats.poisson.ppf(1- (1 - percentile/100.)/2., test_results[i].test_distribution[1])
+                phigh97 = scipy.stats.poisson.ppf(1 - (1 - percentile/100.)/2., test_results[i].test_distribution[1])
                 low97 = test_results[i].observed_statistic - plow97
                 high97 = phigh97 - test_results[i].observed_statistic
                 ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) - i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
                             color='slategray', alpha=1.0, zorder=0)
                 p_values.append(test_results[i].quantile[1] * 2.0)
-                        
-            if p_values[i] < 10e-5:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
-    
-            if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 0.0125 and p_values[i] < 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
-    
-            if p_values[i] >= 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)
-    
-    
+                if p_values[i] < 10e-5:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='red', markersize=8, zorder=2)
+                elif p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='#FF7F50', markersize=8, zorder=2)
+                elif p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='gold', markersize=8, zorder=2)
+                elif p_values[i] >= 10e-3 and p_values[i] < 0.0125:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='white', markersize=8, zorder=2)
+                elif p_values[i] >= 0.0125 and p_values[i] < 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='skyblue', markersize=8, zorder=2)
+                elif p_values[i] >= 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='blue', markersize=8, zorder=2)
+    # Operate on all other consistency tests
     else:
         for i in range(len(test_results)):
             plow97 = numpy.percentile(test_results[i].test_distribution, 2.5)
-            phigh97 = numpy.percentile(test_results[i].test_distribution, 100)
+            phigh97 = numpy.percentile(test_results[i].test_distribution, 97.5)
             low97 = test_results[i].observed_statistic - plow97
             high97 = phigh97 - test_results[i].observed_statistic  
             ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) -i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
                         color='slategray', alpha=1.0, zorder=0)
             p_values.append(test_results[i].quantile)
 
-        if p_values[i] < 10e-5:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
-    
-        if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
-        
-        if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
-        
-        if p_values[i] >= 10e-3  and p_values[i] < 0.025:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
-        
-        if p_values[i] >= 0.025 and p_values[i] < 0.05:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
-    
-        if p_values[i] >= 0.05:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)  
+            if p_values[i] < 10e-5:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='red', markersize=8, zorder=2)
+            elif p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='#FF7F50', markersize=8, zorder=2)
+            elif p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='gold', markersize=8, zorder=2)
+            elif p_values[i] >= 10e-3  and p_values[i] < 0.025:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='white', markersize=8, zorder=2)
+            elif p_values[i] >= 0.025 and p_values[i] < 0.05:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='skyblue', markersize=8, zorder=2)
+            elif p_values[i] >= 0.05:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='blue', markersize=8, zorder=2)
     
-        legend_elements = [Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.025 $\leq$ p < 0.05', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.05', markersize=10, markeredgecolor='k')]
+        legend_elements = [
+            matplotlib.lines.Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.025 $\leq$ p < 0.05', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.05', markersize=10, markeredgecolor='k')]
 
         ax.legend(handles=legend_elements, loc=4, fontsize=13, edgecolor='k') 
     

From 862472431410708c3b75387ebd34cd14c4f81ef6 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 10:54:51 -0700
Subject: [PATCH 07/29] fixed failing test with python 3.10 due to floating
 point rounding issue

---
 tests/test_csep1_evaluations.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/tests/test_csep1_evaluations.py b/tests/test_csep1_evaluations.py
index a733003f..b870ef6a 100644
--- a/tests/test_csep1_evaluations.py
+++ b/tests/test_csep1_evaluations.py
@@ -125,9 +125,9 @@ def test_t_test(self):
                            'information_gain': 0.08052612477654024,
                            'ig_lower': -0.029435677283374914,
                            'ig_upper': 0.19048792683645538}
-
-        print('T Test: Running Unit Test')
-        self.assertEqual(_t_test_ndarray(forecast_A, forecast_B, numpy.sum(obs), forecast_A.sum(), forecast_B.sum()), t_test_expected, 'Failed T Test')
+        numpy.testing.assert_allclose(
+            _t_test_ndarray(forecast_A, forecast_B, numpy.sum(obs), forecast_A.sum(), forecast_B.sum()),
+            t_test_expected)
 
 
 if __name__ == '__main__':

From 1a507f99aa41e55b080195e170a7c8ea1eb21040 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 11:22:10 -0700
Subject: [PATCH 08/29] fixed warnings from numpy np.int -> np.int64 minor code
 formatting updates update tests for python 3.10: failing absolute assertion
 changing to numpy.testing.all_close in csep1 t-test

---
 csep/core/regions.py            |  4 ++--
 csep/utils/basic_types.py       |  2 +-
 csep/utils/calc.py              | 14 +++++++-------
 tests/test_csep1_evaluations.py | 23 ++++++++++++-----------
 4 files changed, 22 insertions(+), 21 deletions(-)

diff --git a/csep/core/regions.py b/csep/core/regions.py
index 05c69747..4ad79235 100644
--- a/csep/core/regions.py
+++ b/csep/core/regions.py
@@ -545,14 +545,14 @@ def get_index_of(self, lons, lats):
             raise ValueError("at least one lon and lat pair contain values that are outside of the valid region.")
         if numpy.any(self.bbox_mask[idy, idx] == 1):
             raise ValueError("at least one lon and lat pair contain values that are outside of the valid region.")
-        return self.idx_map[idy,idx].astype(numpy.int)
+        return self.idx_map[idy, idx].astype(numpy.int64)
 
     def get_location_of(self, indices):
         """
         Returns the polygon associated with the index idx.
 
         Args:
-            idx: index of polygon in region
+            indices: index of polygon in region
 
         Returns:
             Polygon
diff --git a/csep/utils/basic_types.py b/csep/utils/basic_types.py
index 5e1f5aa5..c8c5168e 100644
--- a/csep/utils/basic_types.py
+++ b/csep/utils/basic_types.py
@@ -51,7 +51,7 @@ def add(self, data):
 
         # need to know the range of the data to be inserted on discretized grid (min, max)
         # this is to determine the discretization of the data
-        eps=np.finfo(np.float).eps
+        eps = np.finfo(np.float64).eps
         disc_min = np.floor((data_min+eps-self.anchor)*self.rec_dh)/self.rec_dh+self.anchor
         disc_max = np.ceil((data_max+eps-self.anchor)*self.rec_dh)/self.rec_dh+self.anchor
 
diff --git a/csep/utils/calc.py b/csep/utils/calc.py
index e0071f47..dc208cda 100644
--- a/csep/utils/calc.py
+++ b/csep/utils/calc.py
@@ -79,9 +79,9 @@ def bin1d_vec(p, bins, tol=None, right_continuous=False):
     else:
         h = bins[1] - bins[0]
 
-    a0_tol = numpy.abs(a0) * numpy.finfo(numpy.float).eps
-    h_tol = numpy.abs(h) * numpy.finfo(numpy.float).eps
-    p_tol = numpy.abs(p) * numpy.finfo(numpy.float).eps
+    a0_tol = numpy.abs(a0) * numpy.finfo(numpy.float64).eps
+    h_tol = numpy.abs(h) * numpy.finfo(numpy.float64).eps
+    p_tol = numpy.abs(p) * numpy.finfo(numpy.float64).eps
 
     # absolute tolerance
     if tol is None:
@@ -97,7 +97,7 @@ def bin1d_vec(p, bins, tol=None, right_continuous=False):
         try:
             idx[(idx < 0)] = -1
             idx[(idx >= len(bins) - 1)] = len(bins) - 1
-        except (TypeError):
+        except TypeError:
             if idx >= len(bins) - 1:
                 idx = len(bins) - 1
             if idx < 0:
@@ -105,12 +105,12 @@ def bin1d_vec(p, bins, tol=None, right_continuous=False):
     else:
         try:
             idx[((idx < 0) | (idx >= len(bins)))] = -1
-        except (TypeError):
+        except TypeError:
             if idx < 0 or idx >= len(bins):
                 idx = -1
     try:
-        idx = idx.astype(numpy.int)
-    except (AttributeError):
+        idx = idx.astype(numpy.int64)
+    except AttributeError:
         idx = int(idx)
     return idx
 
diff --git a/tests/test_csep1_evaluations.py b/tests/test_csep1_evaluations.py
index b870ef6a..d095e677 100644
--- a/tests/test_csep1_evaluations.py
+++ b/tests/test_csep1_evaluations.py
@@ -21,6 +21,7 @@ def get_datadir():
     data_dir = os.path.join(root_dir, 'artifacts', 'example_csep1_forecasts')
     return data_dir
 
+
 class TestCSEP1NTestThreeMonthsEEPAS(unittest.TestCase):
 
     def __init__(self, *args, **kwargs):
@@ -61,8 +62,8 @@ def test_ntest_three_months_eepas_model(self):
         test_evaluation_dict['event_count_forecast'] = fore.event_count
         test_evaluation_dict['event_count'] = cata.event_count
         # comparing floats, so we will just map to ndarray and use allclose
-        expected = numpy.array([v for k,v in result_dict.items()])
-        computed = numpy.array([v for k,v in test_evaluation_dict.items()])
+        expected = numpy.array([v for k, v in result_dict.items()])
+        computed = numpy.array([v for k, v in test_evaluation_dict.items()])
         numpy.testing.assert_allclose(expected, computed, rtol=1e-5)
 
 
@@ -82,13 +83,13 @@ def _parse_xml_result(self):
             xml_result['event_count'] = float(child.find('ns0:eventCount', ns).text)
         return xml_result
 
-class TestGriddedForecastTests(unittest.TestCase):
 
+class TestGriddedForecastTests(unittest.TestCase):
 
     def test_n_test(self):
-        forecast = numpy.zeros((10,10))+0.0015
+        forecast = numpy.zeros((10, 10))+0.0015
         forecast = forecast / forecast.size
-        observation = numpy.zeros((10,10))
+        observation = numpy.zeros((10, 10))
         expected_output = (1.0, 0.9985011244377109)
         print('N Test: Running Unit Test')
         numpy.testing.assert_allclose(_number_test_ndarray(forecast.sum(), observation.sum()), expected_output)
@@ -116,18 +117,18 @@ def test_t_test(self):
         the equations from
 
         """
-        forecast_A = numpy.array([[8, 2], [3, 5]])
-        forecast_B = numpy.array([[6, 4], [2, 8]])
+        forecast_a = numpy.array([[8, 2], [3, 5]])
+        forecast_b = numpy.array([[6, 4], [2, 8]])
         obs = numpy.array([[5, 8], [4, 2]])
 
-        t_test_expected = {'t_critical': 2.10092204024096,
-                           't_statistic': 1.5385261717159382,
+        t_test_expected = {'t_statistic': 1.5385261717159382,
+                           't_critical': 2.10092204024096,
                            'information_gain': 0.08052612477654024,
                            'ig_lower': -0.029435677283374914,
                            'ig_upper': 0.19048792683645538}
         numpy.testing.assert_allclose(
-            _t_test_ndarray(forecast_A, forecast_B, numpy.sum(obs), forecast_A.sum(), forecast_B.sum()),
-            t_test_expected)
+            [v for k, v in _t_test_ndarray(forecast_a, forecast_b, numpy.sum(obs), forecast_a.sum(), forecast_b.sum()).items()],
+            [v for k, v in t_test_expected.items()])
 
 
 if __name__ == '__main__':

From affb7e86aa632d40907004e18f2f4f5422b63419 Mon Sep 17 00:00:00 2001
From: bayonato89 <72937672+bayonato89@users.noreply.github.com>
Date: Thu, 18 Aug 2022 19:01:51 +0100
Subject: [PATCH 09/29] Non poissonian tests (#189)

* Changed np for numpy in the poisson_evaluations.py file
* Added non-Poissonian comparative and consistency tests.
* format  docstrings
* Rename non_poissonian_evaluations.py to binomial_evaluations.py
* Update binomial_evaluations.py
removed unused imports

Co-authored-by: wsavran <35315438+wsavran@users.noreply.github.com>
---
 csep/core/binomial_evaluations.py | 372 ++++++++++++++++++++++++++++++
 1 file changed, 372 insertions(+)
 create mode 100644 csep/core/binomial_evaluations.py

diff --git a/csep/core/binomial_evaluations.py b/csep/core/binomial_evaluations.py
new file mode 100644
index 00000000..9ecd61ea
--- /dev/null
+++ b/csep/core/binomial_evaluations.py
@@ -0,0 +1,372 @@
+import numpy
+import scipy.stats
+import scipy.spatial
+
+from csep.models import EvaluationResult
+from csep.core.exceptions import CSEPCatalogException
+
+def _nbd_number_test_ndarray(fore_cnt, obs_cnt, variance, epsilon=1e-6):
+    """ Computes delta1 and delta2 values from the Negative Binomial (NBD) number test.
+
+    Args:
+        fore_cnt (float): parameter of negative binomial distribution coming from expected value of the forecast
+        obs_cnt (float): count of earthquakes observed during the testing period.
+        variance (float): variance parameter of negative binomial distribution coming from historical catalog. 
+        A variance value of approximately 23541 has been calculated using M5.95+ earthquakes observed worldwide from 1982 to 2013.
+        epsilon (float): tolerance level to satisfy the requirements of two-sided p-value
+
+    Returns
+        result (tuple): (delta1, delta2)
+    """
+    var = variance
+    mean = fore_cnt
+    upsilon = 1.0 - ((var - mean) / var)
+    tau = (mean**2 /(var - mean))
+    
+    delta1 = 1.0 - scipy.stats.nbinom.cdf(obs_cnt - epsilon, tau, upsilon, loc=0)
+    delta2 = scipy.stats.nbinom.cdf(obs_cnt + epsilon, tau, upsilon, loc=0)
+
+    return delta1, delta2
+
+    
+def negative_binomial_number_test(gridded_forecast, observed_catalog, variance):
+    """ Computes "negative binomial N-Test" on a gridded forecast.
+
+    Computes Number (N) test for Observed and Forecasts. Both data sets are expected to be in terms of event counts.
+    We find the Total number of events in Observed Catalog and Forecasted Catalogs. Which are then employed to compute the 
+    probablities of
+    (i) At least no. of events (delta 1)
+    (ii) At most no. of events (delta 2) assuming the negative binomial distribution.
+
+    Args:
+        gridded_forecast:   Forecast of a Model (Gridded) (Numpy Array)
+                    A forecast has to be in terms of Average Number of Events in Each Bin
+                    It can be anything greater than zero
+        observed_catalog:   Observed (Gridded) seismicity (Numpy Array):
+                    An Observation has to be Number of Events in Each Bin
+                    It has to be a either zero or positive integer only (No Floating Point)
+        variance:   Variance parameter of negative binomial distribution obtained from historical catalog.            
+
+    Returns:
+        out (tuple): (delta_1, delta_2)
+    """
+    result = EvaluationResult()
+
+    # observed count
+    obs_cnt = observed_catalog.event_count
+
+    # forecasts provide the expeceted number of events during the time horizon of the forecast
+    fore_cnt = gridded_forecast.event_count
+
+    epsilon = 1e-6
+
+    # stores the actual result of the number test
+    delta1, delta2 = _nbd_number_test_ndarray(fore_cnt, obs_cnt, variance, epsilon=epsilon)
+    
+    # store results
+    result.test_distribution = ('negative_binomial', fore_cnt)
+    result.name = 'NBD N-Test'
+    result.observed_statistic = obs_cnt
+    result.quantile = (delta1, delta2)
+    result.sim_name = gridded_forecast.name
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    result.min_mw = numpy.min(gridded_forecast.magnitudes)
+
+    return result
+  
+    
+def binary_joint_log_likelihood_ndarray(forecast, catalog):
+    """ Computes Bernoulli log-likelihood scores, assuming that earthquakes follow a binomial distribution.
+    
+    Args:
+        forecast:   Forecast of a Model (Gridded) (Numpy Array)
+                    A forecast has to be in terms of Average Number of Events in Each Bin
+                    It can be anything greater than zero
+        catalog:    Observed (Gridded) seismicity (Numpy Array):
+                    An Observation has to be Number of Events in Each Bin
+                    It has to be a either zero or positive integer only (No Floating Point)
+    """
+    #First, we mask the forecast in cells where we could find log=0.0 singularities:
+    forecast_masked = np.ma.masked_where(forecast.ravel() <= 0.0, forecast.ravel()) 
+    
+    #Then, we compute the log-likelihood of observing one or more events given a Poisson distribution, i.e., 1 - Pr(0) 
+    target_idx = numpy.nonzero(catalog.ravel())
+    y = numpy.zeros(forecast_masked.ravel().shape)
+    y[target_idx[0]] = 1
+    first_term = y * (np.log(1.0 - np.exp(-forecast_masked.ravel())))
+    
+    #Also, we estimate the log-likelihood in cells no events are observed:
+    second_term = (1-y) * (-forecast_masked.ravel().data)
+    #Finally, we sum both terms to compute the joint log-likelihood score:
+    return sum(first_term.data + second_term.data)
+    
+    
+def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000, random_numbers=None, 
+                              seed=None, use_observed_counts=True, verbose=True, normalize_likelihood=False):
+    """  Computes binary conditional-likelihood test from CSEP using an efficient simulation based approach.
+    
+    Args:
+        forecast_data (numpy.ndarray): nd array where [:, -1] are the magnitude bins.
+        observed_data (numpy.ndarray): same format as observation.
+        num_simulations: default number of simulations to use for likelihood based simulations
+        seed: used for reproducibility of the prng
+        random_numbers (numpy.ndarray): can supply an explicit list of random numbers, primarily used for software testing
+        use_observed_counts (bool): if true, will simulate catalogs using the observed events, if false will draw from poisson 
+        distribution
+    """
+    
+    # Array-masking that avoids log singularities:
+    forecast_data = numpy.ma.masked_where(forecast_data <= 0.0, forecast_data) 
+    
+    # set seed for the likelihood test
+    if seed is not None:
+        numpy.random.seed(seed)
+
+    # used to determine where simulated earthquake should be placed, by definition of cumsum these are sorted
+    sampling_weights = numpy.cumsum(forecast_data.ravel()) / numpy.sum(forecast_data)
+
+    # data structures to store results
+    sim_fore = numpy.zeros(sampling_weights.shape)
+    simulated_ll = []
+    n_obs = len(np.unique(np.nonzero(observed_data.ravel())))
+    n_fore = numpy.sum(forecast_data)
+    expected_forecast_count = int(n_obs) 
+    
+    if use_observed_counts and normalize_likelihood:
+        scale = n_obs / n_fore
+        expected_forecast_count = int(n_obs)
+        forecast_data = scale * forecast_data
+
+    # main simulation step in this loop
+    for idx in range(num_simulations):
+        if use_observed_counts:
+            num_events_to_simulate = int(n_obs)
+        else:
+            num_events_to_simulate = int(numpy.random.poisson(expected_forecast_count))
+    
+        if random_numbers is None:
+            sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore)
+        else:
+            sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore,
+                                         random_numbers=random_numbers[idx,:])
+
+    
+        # compute joint log-likelihood
+        current_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, sim_fore)
+        
+        # append to list of simulated log-likelihoods
+        simulated_ll.append(current_ll)
+
+        # just be verbose
+        if verbose:
+            if (idx + 1) % 100 == 0:
+                print(f'... {idx + 1} catalogs simulated.')
+                
+                target_idx = numpy.nonzero(catalog.ravel())
+
+    # observed joint log-likelihood
+    obs_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, observed_data)
+        
+    # quantile score
+    qs = numpy.sum(simulated_ll <= obs_ll) / num_simulations
+
+    # float, float, list
+    return qs, obs_ll, simulated_ll
+ 
+    
+def binary_spatial_test(gridded_forecast, observed_catalog, num_simulations=1000, seed=None, random_numbers=None, verbose=False):
+    """  Performs the binary spatial test on the Forecast using the Observed Catalogs.
+    
+    Note: The forecast and the observations should be scaled to the same time period before calling this function. This increases
+    transparency as no assumptions are being made about the length of the forecasts. This is particularly important for
+    gridded forecasts that supply their forecasts as rates.
+    
+    Args:
+        gridded_forecast: csep.core.forecasts.GriddedForecast
+        observed_catalog: csep.core.catalogs.Catalog
+        num_simulations (int): number of simulations used to compute the quantile score
+        seed (int): used fore reproducibility, and testing
+        random_numbers (numpy.ndarray): random numbers used to override the random number generation. injection point for testing.
+        
+    Returns:
+        evaluation_result: csep.core.evaluations.EvaluationResult
+    """
+
+    # grid catalog onto spatial grid
+    gridded_catalog_data = observed_catalog.spatial_counts()
+
+    # simply call likelihood test on catalog data and forecast
+    qs, obs_ll, simulated_ll = _binary_likelihood_test(gridded_forecast.spatial_counts(), gridded_catalog_data,
+                                                        num_simulations=num_simulations,
+                                                        seed=seed,
+                                                        random_numbers=random_numbers,
+                                                        use_observed_counts=True,
+                                                        verbose=verbose, normalize_likelihood=True)
+
+    
+# populate result data structure
+    result = EvaluationResult()
+    result.test_distribution = simulated_ll
+    result.name = 'Binary S-Test'
+    result.observed_statistic = obs_ll
+    result.quantile = qs
+    result.sim_name = gridded_forecast.name
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    try:
+        result.min_mw = numpy.min(gridded_forecast.magnitudes)
+    except AttributeError:
+        result.min_mw = -1
+    return result
+    
+    
+def binary_conditional_likelihood_test(gridded_forecast, observed_catalog, num_simulations=1000, seed=None, random_numbers=None, verbose=False):
+    """ Performs the binary conditional likelihood test on Gridded Forecast using an Observed Catalog.
+
+    Normalizes the forecast so the forecasted rate are consistent with the observations. This modification
+    eliminates the strong impact differences in the number distribution have on the forecasted rates.
+
+    Note: The forecast and the observations should be scaled to the same time period before calling this function. This increases
+    transparency as no assumptions are being made about the length of the forecasts. This is particularly important for
+    gridded forecasts that supply their forecasts as rates.
+
+    Args:
+        gridded_forecast: csep.core.forecasts.GriddedForecast
+        observed_catalog: csep.core.catalogs.Catalog
+        num_simulations (int): number of simulations used to compute the quantile score
+        seed (int): used fore reproducibility, and testing
+        random_numbers (numpy.ndarray): random numbers used to override the random number generation. injection point for testing.
+
+    Returns:
+        evaluation_result: csep.core.evaluations.EvaluationResult
+    """
+        
+    # grid catalog onto spatial grid
+    try:
+        _ = observed_catalog.region.magnitudes
+    except CSEPCatalogException:
+        observed_catalog.region = gridded_forecast.region
+    gridded_catalog_data = observed_catalog.spatial_magnitude_counts()
+
+    # simply call likelihood test on catalog data and forecast
+    qs, obs_ll, simulated_ll = _binary_likelihood_test(gridded_forecast.data, gridded_catalog_data,
+                                                        num_simulations=num_simulations, seed=seed, random_numbers=random_numbers,
+                                                        use_observed_counts=True,
+                                                        verbose=verbose, normalize_likelihood=False)
+
+    # populate result data structure
+    result = EvaluationResult()
+    result.test_distribution = simulated_ll
+    result.name = 'Binary CL-Test'
+    result.observed_statistic = obs_ll
+    result.quantile = qs
+    result.sim_name = gridded_forecast.name
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    result.min_mw = numpy.min(gridded_forecast.magnitudes)
+
+    return result
+     
+    
+def matrix_binary_t_test(target_event_rates1, target_event_rates2, n_obs, n_f1, n_f2, catalog, alpha=0.05):
+    """ Computes binary T test statistic by comparing two target event rate distributions.
+
+    We compare Forecast from Model 1 and with Forecast of Model 2. Information Gain per Active Bin (IGPA) is computed, which is then 
+    employed to compute T statistic. Confidence interval of Information Gain can be computed using T_critical. For a complete 
+    explanation see Rhoades, D. A., et al., (2011). Efficient testing of earthquake forecasting models. Acta Geophysica, 59(4), 
+    728-747. doi:10.2478/s11600-011-0013-5, and Bayona J.A. et al., (2022). Prospective evaluation of multiplicative hybrid earthquake 
+    forecasting models in California. doi: 10.1093/gji/ggac018.
+    
+    Args:
+        target_event_rates1 (numpy.ndarray): nd-array storing target event rates
+        target_event_rates2 (numpy.ndarray): nd-array storing target event rates
+        n_obs (float, int, numpy.ndarray): number of observed earthquakes, should be whole number and >= zero.
+        n_f1 (float): Total number of forecasted earthquakes by Model 1
+        n_f2 (float): Total number of forecasted earthquakes by Model 2
+        catalog: csep.core.catalogs.Catalog
+        alpha (float): tolerance level for the type-i error rate of the statistical test
+
+    Returns:
+        out (dict): relevant statistics from the t-test
+    """
+    # Some Pre Calculations -  Because they are being used repeatedly.
+    N_p = n_obs  
+    N = len(np.unique(np.nonzero(catalog.spatial_magnitude_counts().ravel()))) # Number of active bins
+    N1 = n_f1  
+    N2 = n_f2  
+    X1 = numpy.log(target_event_rates1)  # Log of every element of Forecast 1
+    X2 = numpy.log(target_event_rates2)  # Log of every element of Forecast 2
+    
+
+    # Information Gain, using Equation (17)  of Rhoades et al. 2011
+    information_gain = (numpy.sum(X1 - X2) - (N1 - N2)) / N
+
+    # Compute variance of (X1-X2) using Equation (18)  of Rhoades et al. 2011
+    first_term = (numpy.sum(numpy.power((X1 - X2), 2))) / (N - 1)
+    second_term = numpy.power(numpy.sum(X1 - X2), 2) / (numpy.power(N, 2) - N)
+    forecast_variance = first_term - second_term
+
+    forecast_std = numpy.sqrt(forecast_variance)
+    t_statistic = information_gain / (forecast_std / numpy.sqrt(N))
+
+    # Obtaining the Critical Value of T from T distribution.
+    df = N - 1
+    t_critical = scipy.stats.t.ppf(1 - (alpha / 2), df)  # Assuming 2-Tail Distribution  for 2 tail, divide 0.05/2.
+
+    # Computing Information Gain Interval.
+    ig_lower = information_gain - (t_critical * forecast_std / numpy.sqrt(N))
+    ig_upper = information_gain + (t_critical * forecast_std / numpy.sqrt(N))
+
+    # If T value greater than T critical, Then both Lower and Upper Confidence Interval limits will be greater than Zero.
+    # If above Happens, Then It means that Forecasting Model 1 is better than Forecasting Model 2.
+    return {'t_statistic': t_statistic,
+            't_critical': t_critical,
+            'information_gain': information_gain,
+            'ig_lower': ig_lower,
+            'ig_upper': ig_upper}
+    
+
+def binary_paired_t_test(forecast, benchmark_forecast, observed_catalog, alpha=0.05, scale=False):
+    """ Computes the binary t-test for gridded earthquake forecasts.
+
+    This score is positively oriented, meaning that positive values of the information gain indicate that the
+    forecast is performing better than the benchmark forecast.
+
+    Args:
+        forecast (csep.core.forecasts.GriddedForecast): nd-array storing gridded rates, axis=-1 should be the magnitude column
+        benchmark_forecast (csep.core.forecasts.GriddedForecast): nd-array storing gridded rates, axis=-1 should be the magnitude 
+        column
+        observed_catalog (csep.core.catalogs.AbstractBaseCatalog): number of observed earthquakes, should be whole number and >= zero.
+        alpha (float): tolerance level for the type-i error rate of the statistical test
+        scale (bool): if true, scale forecasted rates down to a single day
+
+    Returns:
+        evaluation_result: csep.core.evaluations.EvaluationResult
+    """
+
+    # needs some pre-processing to put the forecasts in the context that is required for the t-test. this is different
+    # for cumulative forecasts (eg, multiple time-horizons) and static file-based forecasts.
+    target_event_rate_forecast1p, n_fore1 = forecast.target_event_rates(observed_catalog, scale=scale)
+    target_event_rate_forecast2p, n_fore2 = benchmark_forecast.target_event_rates(observed_catalog, scale=scale)
+    
+    target_event_rate_forecast1 = forecast.data.ravel()[np.unique(np.nonzero(observed_catalog.spatial_magnitude_counts().ravel()))]
+    target_event_rate_forecast2 = benchmark_forecast.data.ravel()[np.unique(np.nonzero(observed_catalog.spatial_magnitude_counts().
+    ravel()))]
+
+    # call the primative version operating on ndarray
+    out = matrix_binary_t_test(target_event_rate_forecast1, target_event_rate_forecast2, observed_catalog.event_count, n_fore1, n_fore2,
+                          observed_catalog,
+                          alpha=alpha)
+
+    # storing this for later
+    result = EvaluationResult()
+    result.name = 'binary paired T-Test'
+    result.test_distribution = (out['ig_lower'], out['ig_upper'])
+    result.observed_statistic = out['information_gain']
+    result.quantile = (out['t_statistic'], out['t_critical'])
+    result.sim_name = (forecast.name, benchmark_forecast.name)
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    result.min_mw = np.min(forecast.magnitudes)
+    return result

From 518e750ecb570365af4ce8d0b5cda133c6877cb4 Mon Sep 17 00:00:00 2001
From: Pablo Iturrieta <69042881+pabloitu@users.noreply.github.com>
Date: Tue, 20 Sep 2022 19:56:59 +0200
Subject: [PATCH 10/29] Added NZ testing and collection regions, parser and
 test (#198)

Added NZ collection and testing regions, and parser to csep region object.
Added test for NZ testing regions
---
 .../artifacts/Regions/nz.collection.nodes.dat | 9029 +++++++++++++++++
 csep/artifacts/Regions/nz.testing.nodes.dat   | 6343 ++++++++++++
 csep/core/regions.py                          |   84 +
 tests/artifacts/regions/NZTestArea.dat        | 6343 ++++++++++++
 tests/test_regions.py                         |   31 +-
 5 files changed, 21828 insertions(+), 2 deletions(-)
 create mode 100644 csep/artifacts/Regions/nz.collection.nodes.dat
 create mode 100644 csep/artifacts/Regions/nz.testing.nodes.dat
 create mode 100644 tests/artifacts/regions/NZTestArea.dat

diff --git a/csep/artifacts/Regions/nz.collection.nodes.dat b/csep/artifacts/Regions/nz.collection.nodes.dat
new file mode 100644
index 00000000..6dd942d5
--- /dev/null
+++ b/csep/artifacts/Regions/nz.collection.nodes.dat
@@ -0,0 +1,9029 @@
+172.65    -33.45
+172.75    -33.45
+172.85    -33.45
+172.95    -33.45
+173.05    -33.45
+173.15    -33.45
+173.25    -33.45
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+172.35    -33.55
+172.45    -33.55
+172.55    -33.55
+172.65    -33.55
+172.75    -33.55
+172.85    -33.55
+172.95    -33.55
+173.05    -33.55
+173.15    -33.55
+173.25    -33.55
+173.35    -33.55
+173.45    -33.55
+172.05    -33.65
+172.15    -33.65
+172.25    -33.65
+172.35    -33.65
+172.45    -33.65
+172.55    -33.65
+172.65    -33.65
+172.75    -33.65
+172.85    -33.65
+172.95    -33.65
+173.05    -33.65
+173.15    -33.65
+173.25    -33.65
+173.35    -33.65
+173.45    -33.65
+173.55    -33.65
+171.95    -33.75
+172.05    -33.75
+172.15    -33.75
+172.25    -33.75
+172.35    -33.75
+172.45    -33.75
+172.55    -33.75
+172.65    -33.75
+172.75    -33.75
+172.85    -33.75
+172.95    -33.75
+173.05    -33.75
+173.15    -33.75
+173.25    -33.75
+173.35    -33.75
+173.45    -33.75
+173.55    -33.75
+173.65    -33.75
+173.75    -33.75
+171.85    -33.85
+171.95    -33.85
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diff --git a/csep/artifacts/Regions/nz.testing.nodes.dat b/csep/artifacts/Regions/nz.testing.nodes.dat
new file mode 100644
index 00000000..c4e876b9
--- /dev/null
+++ b/csep/artifacts/Regions/nz.testing.nodes.dat
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diff --git a/csep/core/regions.py b/csep/core/regions.py
index 05c69747..73aa9123 100644
--- a/csep/core/regions.py
+++ b/csep/core/regions.py
@@ -192,6 +192,90 @@ def italy_csep_collection_region(dh_scale=1, magnitudes=None, name="csep-italy-c
 
     return relm_region
 
+def nz_csep_region(dh_scale=1, magnitudes=None, name="csep-nz", use_midpoint=True):
+    """ Return collection region for the New Zealand CSEP testing region
+
+    Args:
+        dh_scale (int): factor of two multiple to change the grid size
+        mangitudes (array-like): array representing the lower bin edges of the magnitude bins
+        name (str): human readable identifer
+        use_midpoints (bool): if true, treat values in file as midpoints. default = true.
+
+    Returns:
+        :class:`csep.core.spatial.CartesianGrid2D`
+
+    Raises:
+        ValueError: dh_scale must be a factor of two
+
+    """
+    if dh_scale % 2 != 0 and dh_scale != 1:
+        raise ValueError("dh_scale must be a factor of two or dh_scale must equal unity.")
+
+    # we can hard-code the dh because we hard-code the filename
+    dh = 0.1
+    root_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+    filepath = os.path.join(root_dir, 'artifacts', 'Regions', 'nz.testing.nodes.dat')
+    points = numpy.loadtxt(filepath)
+    if use_midpoint:
+        origins = numpy.array(points) - dh / 2
+    else:
+        origins = numpy.array(points)
+
+    if dh_scale > 1:
+        origins = increase_grid_resolution(origins, dh, dh_scale)
+        dh = dh / dh_scale
+
+    # turn points into polygons and make region object
+    bboxes = compute_vertices(origins, dh)
+    nz_region = CartesianGrid2D([Polygon(bbox) for bbox in bboxes], dh, name=name)
+
+    if magnitudes is not None:
+        nz_region.magnitudes = magnitudes
+
+    return nz_region
+
+def nz_csep_collection_region(dh_scale=1, magnitudes=None, name="csep-nz-collection", use_midpoint=True):
+    """ Return collection region for the New Zealand CSEP collection region
+
+    Args:
+        dh_scale (int): factor of two multiple to change the grid size
+        mangitudes (array-like): array representing the lower bin edges of the magnitude bins
+        name (str): human readable identifer
+        use_midpoints (bool): if true, treat values in file as midpoints. default = true.
+
+    Returns:
+        :class:`csep.core.spatial.CartesianGrid2D`
+
+    Raises:
+        ValueError: dh_scale must be a factor of two
+
+    """
+    if dh_scale % 2 != 0 and dh_scale != 1:
+        raise ValueError("dh_scale must be a factor of two or dh_scale must equal unity.")
+
+    # we can hard-code the dh because we hard-code the filename
+    dh = 0.1
+    root_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+    filepath = os.path.join(root_dir, 'artifacts', 'Regions', 'nz.collection.nodes.dat')
+    points = numpy.loadtxt(filepath)
+    if use_midpoint:
+        origins = numpy.array(points) - dh / 2
+    else:
+        origins = numpy.array(points)
+
+    if dh_scale > 1:
+        origins = increase_grid_resolution(origins, dh, dh_scale)
+        dh = dh / dh_scale
+
+    # turn points into polygons and make region object
+    bboxes = compute_vertices(origins, dh)
+    nz_collection_region = CartesianGrid2D([Polygon(bbox) for bbox in bboxes], dh, name=name)
+
+    if magnitudes is not None:
+        nz_collection_region.magnitudes = magnitudes
+
+    return nz_collection_region
+
 def global_region(dh=0.1, name="global", magnitudes=None):
     """ Creates a global region used for evaluating gridded forecasts on the global scale.
 
diff --git a/tests/artifacts/regions/NZTestArea.dat b/tests/artifacts/regions/NZTestArea.dat
new file mode 100644
index 00000000..c4e876b9
--- /dev/null
+++ b/tests/artifacts/regions/NZTestArea.dat
@@ -0,0 +1,6343 @@
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+178.85    -37.45
+178.85    -37.35
+178.95    -38.45
+178.95    -38.35
+178.95    -38.25
+178.95    -38.15
+178.95    -38.05
+178.95    -37.95
+178.95    -37.85
+178.95    -37.75
+178.95    -37.65
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+178.95    -37.45
+178.95    -37.35
+179.05    -38.05
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+179.05    -37.75
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+179.15    -37.65
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diff --git a/tests/test_regions.py b/tests/test_regions.py
index ac5921ec..a1e2cced 100644
--- a/tests/test_regions.py
+++ b/tests/test_regions.py
@@ -3,7 +3,7 @@
 
 import numpy
 
-from csep.core.regions import italy_csep_region, california_relm_region
+from csep.core.regions import italy_csep_region, california_relm_region, nz_csep_region
 
 def get_italy_region_fname():
     root_dir = os.path.dirname(os.path.abspath(__file__))
@@ -15,6 +15,11 @@ def get_california_region_fname():
     data_dir = os.path.join(root_dir, 'artifacts', 'regions', 'RELMTestArea.dat')
     return data_dir
 
+def get_nz_region_fname():
+    root_dir = os.path.dirname(os.path.abspath(__file__))
+    data_dir = os.path.join(root_dir, 'artifacts', 'regions', 'NZTestArea.dat')
+    return data_dir
+
 class TestItalyRegion(unittest.TestCase):
 
     def __init__(self, *args, **kwargs):
@@ -58,4 +63,26 @@ def test_origins(self):
 
     def test_eq_oper(self):
         r = california_relm_region()
-        assert self.r == r
\ No newline at end of file
+        assert self.r == r
+
+class TestNZRegion(unittest.TestCase):
+
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+
+    def setUp(self):
+
+        self.from_dat = numpy.loadtxt(get_nz_region_fname())
+        self.num_nodes = len(self.from_dat)
+
+    def test_node_count(self):
+        """ Ensures the node counts are consistent between the two files. """
+        r = nz_csep_region()
+        self.assertEqual(self.num_nodes, r.num_nodes)
+
+
+    def test_origins(self):
+        """ Compares XML file against the simple .dat file containing the region. """
+        r = nz_csep_region()
+        # they dont have to be in the same order, but they need
+        numpy.testing.assert_array_equal(r.midpoints().sort(), self.from_dat.sort())

From bb299b2cfc23bc5e2f61d7a91e67d316fad12bff Mon Sep 17 00:00:00 2001
From: Pablo Iturrieta <69042881+pabloitu@users.noreply.github.com>
Date: Wed, 21 Sep 2022 01:05:02 +0200
Subject: [PATCH 11/29] fix: region border plot (#199)

fix: region border plot. Now uses shapely that merges all cells and gets the boundary of the total region. Bypasses floating point issues by rounding down to 2 decimals
fix: load_ascii now creates cell polygons clockwise
fix: tight_bbox has option for precision. It is not necessary for lat_lon, but explicited the argument, in case cartesian coordinates were implemented.
build: added shapely as requirement
---
 csep/core/forecasts.py | 13 +++++++------
 csep/core/regions.py   | 40 +++++++++++++---------------------------
 requirements.txt       |  1 +
 requirements.yml       |  1 +
 setup.py               |  3 ++-
 5 files changed, 24 insertions(+), 34 deletions(-)

diff --git a/csep/core/forecasts.py b/csep/core/forecasts.py
index 9d6599d9..68cf27e7 100644
--- a/csep/core/forecasts.py
+++ b/csep/core/forecasts.py
@@ -397,22 +397,23 @@ def load_ascii(cls, ascii_fname, start_date=None, end_date=None, name=None, swap
         data = numpy.loadtxt(ascii_fname)
         # this is very ugly, but since unique returns a sorted list, we want to get the index, sort that and then return
         # from the original array. same for magnitudes below.
-        all_polys = data[:,:4]
-        all_poly_mask = data[:,-1]
+        all_polys = data[:, :4]
+        all_poly_mask = data[:, -1]
         sorted_idx = numpy.sort(numpy.unique(all_polys, return_index=True, axis=0)[1], kind='stable')
         unique_poly = all_polys[sorted_idx]
         # gives the flag for a spatial cell in the order it was presented in the file
         poly_mask = all_poly_mask[sorted_idx]
         # create magnitudes bins using Mag_0, ignoring Mag_1 bc they are regular until last bin. we dont want binary search for this
-        all_mws = data[:,-4]
+        all_mws = data[:, -4]
         sorted_idx = numpy.sort(numpy.unique(all_mws, return_index=True)[1], kind='stable')
         mws = all_mws[sorted_idx]
         # csep1 stores the lat lons as min values and not (x,y) tuples
-        bboxes = [tuple(itertools.product(bbox[:2], bbox[2:])) for bbox in unique_poly]
         if swap_latlon:
-            bboxes = [tuple(itertools.product(bbox[2:], bbox[:2])) for bbox in unique_poly]
+            bboxes = [((i[2], i[0]), (i[3], i[0]), (i[3], i[1]), (i[2], i[1])) for i in unique_poly]
+        else:
+            bboxes = [((i[0], i[2]), (i[0], i[3]), (i[1], i[3]), (i[1], i[2])) for i in unique_poly]
         # the spatial cells are arranged fast in latitude, so this only works for the specific csep1 file format
-        dh = float(unique_poly[0,3] - unique_poly[0,2])
+        dh = float(unique_poly[0, 3] - unique_poly[0, 2])
         # create CarteisanGrid of points
         region = CartesianGrid2D([Polygon(bbox) for bbox in bboxes], dh, mask=poly_mask)
         # get dims of 2d np.array
diff --git a/csep/core/regions.py b/csep/core/regions.py
index 73aa9123..e9551f03 100644
--- a/csep/core/regions.py
+++ b/csep/core/regions.py
@@ -8,6 +8,8 @@
 import numpy
 import numpy as np
 import mercantile
+from shapely import geometry
+from shapely.ops import unary_union
 
 # PyCSEP imports
 from csep.utils.calc import bin1d_vec, cleaner_range, first_nonnan, last_nonnan
@@ -806,35 +808,19 @@ def _build_bitmask_vec(self):
 
         return a, xs, ys
 
-    def tight_bbox(self):
-        # creates tight bounding box around the region, probably a faster way to do this.
-        ny, nx = self.idx_map.shape
-        asc = []
-        desc = []
-        for j in range(ny):
-            row = self.idx_map[j, :]
-            argmin = first_nonnan(row)
-            argmax = last_nonnan(row)
-            # points are stored clockwise
-            poly_min = self.polygons[int(row[argmin])].points
-            asc.insert(0, poly_min[0])
-            asc.insert(0, poly_min[1])
-            poly_max = self.polygons[int(row[argmax])].points
-            lat_0 = poly_max[2][1]
-            lat_1 = poly_max[3][1]
-            # last two points are 'right hand side of polygon'
-            if lat_0 < lat_1:
-                desc.append(poly_max[2])
-                desc.append(poly_max[3])
-            else:
-                desc.append(poly_max[3])
-                desc.append(poly_max[2])
-        # close the loop
-        poly = np.array(asc + desc)
+    def tight_bbox(self, precision=4):
+        # creates tight bounding box around the region
+        poly = np.array([i.points for i in self.polygons])
+
         sorted_idx = np.sort(np.unique(poly, return_index=True, axis=0)[1], kind='stable')
         unique_poly = poly[sorted_idx]
-        unique_poly = np.append(unique_poly, [unique_poly[0, :]], axis=0)
-        return unique_poly
+
+        # merges all the cell polygons into one
+        polygons = [geometry.Polygon(np.round(i, precision)) for i in unique_poly]
+        joined_poly = unary_union(polygons)
+        bounds = np.array([i for i in joined_poly.boundary.xy]).T
+
+        return bounds
 
     def get_cell_area(self):
         """ Compute the area of each polygon in sq. kilometers.
diff --git a/requirements.txt b/requirements.txt
index e5f26286..78dfc73b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -9,6 +9,7 @@ python-dateutil
 pytest
 vcrpy
 pytest-cov
+shapely
 sphinx
 sphinx-gallery
 sphinx-rtd-theme
diff --git a/requirements.yml b/requirements.yml
index 75a1c52a..85779ee0 100644
--- a/requirements.yml
+++ b/requirements.yml
@@ -13,6 +13,7 @@ dependencies:
   - python-dateutil
   - pytest
   - cartopy
+  - shapely
   - sphinx
   - sphinx-gallery
   - sphinx_rtd_theme
diff --git a/setup.py b/setup.py
index ae8d3fa3..f11037a0 100644
--- a/setup.py
+++ b/setup.py
@@ -34,7 +34,8 @@ def get_version():
         'obspy',
         'pyproj',
         'python-dateutil',
-        'mercantile'
+        'mercantile',
+        'shapely'
     ],
     extras_require = {
         'test': [

From 4a2e926b7d6aac6ef759040c9daf848f67a36454 Mon Sep 17 00:00:00 2001
From: bayonato89 <72937672+bayonato89@users.noreply.github.com>
Date: Thu, 22 Sep 2022 18:00:40 +0100
Subject: [PATCH 12/29] Notebook documentation (#202)

* Added some documentation on new binary CSEP tests.
---
 notebooks/CSEP_tests.ipynb | 76 +++++++++++++++++++++++++++++++++-----
 1 file changed, 66 insertions(+), 10 deletions(-)

diff --git a/notebooks/CSEP_tests.ipynb b/notebooks/CSEP_tests.ipynb
index da30f86c..b377641c 100644
--- a/notebooks/CSEP_tests.ipynb
+++ b/notebooks/CSEP_tests.ipynb
@@ -72,7 +72,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fetched ComCat catalog in 5.9399449825286865 seconds.\n",
+      "Fetched ComCat catalog in 5.9891064167022705 seconds.\n",
       "\n",
       "Downloaded catalog from ComCat with following parameters\n",
       "Start Date: 2010-01-10 00:27:39.320000+00:00\n",
@@ -134,6 +134,33 @@
     "\n",
     "where $\\lambda(m_i, s_j)$ and $\\omega(m_i, s_j)$ are the expected counts from the forecast and observed counts in cell $m_i, s_j$ respectively. We can calculate the likelihood directly given the forecast and discretised observations.\n",
     "\n",
+    "#### Binary consistency tests\n",
+    "\n",
+    "It is known that the Poisson distribution insufficiently captures the variability of earthquakes, as it could be dispersed with respect to the true distribution of seismicity, especially in the presence of clustered earthquakes (Werner and Sornette, 2008; Lombardi and Marzocchi, 2010; Nandan et al., 2019). Therefore, CSEP has recently introduced a set of new consistency tests based on the negative binomial distribution (NBD) and a binary likelihood function, with the aim of reducing the sensitivity of traditional Poisson-based tests to clustering (Bayona et al., 2022).\n",
+    "\n",
+    "The NBD has been shown to better describe non-declustered seismicity, because it has a greater variance than the Poisson distribution to account for spatiotemporal earthquake clustering (Werner et al., 2011a,b). Hence, one can fit a NBD to the rates of observed earthquakes in each forecast's testing region to evaluate number consistencies between forecasts and observations. The probability mass function of an NBD is defined by:\n",
+    "\n",
+    "$P (\\omega\\hspace{0.1cm}|\\hspace{0.1cm}\\tau, \\nu) = \\frac{\\Gamma(\\tau + \\omega)}{\\Gamma(\\tau)\\omega!} \\nu^\\omega (1-\\nu)^{\\omega},$\n",
+    "\n",
+    "where $\\omega = 0,1,2,...$ is the number of events, $\\tau > 0$ and $0 \\leq \\nu \\leq 1$ are parameters, and $\\Gamma$ is the Gamma function. The mean $\\mu$ and  variance $\\sigma^2$ of the NBD are given by\n",
+    "\n",
+    "$\\mu = \\tau\\frac{1 - \\nu}{\\nu}; \\hspace{0.1cm} \\sigma^2=\\tau \\frac{1 - \\nu}{\\nu^2}$.\n",
+    "\n",
+    "Following the approach by Werner et al. (2011b), one can use the expected number earthquakes by the forecast as the mean and estimate the variance from historical catalogs.\n",
+    "\n",
+    "The binary likelihood function can also make the assumption that earthquakes are Poisson distributed less critical by calculating the probability of observing one or more earthquakes in a forecast cell/bin, rather than the likelihood of observing $\\omega =$ 1,2, .., n events. The probability of observing $\\omega = $ 0 earthquakes given an expected number/rate $\\lambda$, assuming a Poisson distribution, is P$_\\mathrm{0}$ = exp(-$\\lambda)$, while the probability of observing one or more events is P$_\\mathrm{_1}$ = 1 - P$_\\mathrm{0}$ = 1 - exp($-\\lambda)$. Accordingly, one can compute the log-likelihood score in each cell/bin based on the binary (or Bernoulli) distribution as:\n",
+    "\n",
+    "$$ L(\\boldsymbol{\\Omega} | \\boldsymbol{\\Lambda}) = X(m_i, s_j) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} \\mathrm{P_1} + (1 -X(m_i, s_j)) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} \\mathrm{P_0} = X(m_i, s_j) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (1-\\mathrm{exp}(-\\lambda(m_i, s_j))) + (1 -X_i) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (\\mathrm{exp}(-\\lambda(m_i, s_j)))$$\n",
+    "\n",
+    "where the first term represents the contribution to the score if a bin $(m_i, s_j)$ contains one or more events, i.e. $X(m_i, s_j)$ = 1, and the second term is the contribution if that cell/bin contains no earthquakes, i.e. $X(m_i, s_j)$ = 0.\n",
+    "\n",
+    "Similar to the example above, the joint likelihood of observing events in individual bins, based on the binary likelihood function, is the sum of each individual log score, i.e.:\n",
+    "\n",
+    "\n",
+    "$$ L(\\boldsymbol{\\Omega} | \\boldsymbol{\\Lambda})  = \\sum_{m_i , s_j \\in \\boldsymbol{R}} \\hspace{0.05cm}[X(m_i, s_j) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (1-\\mathrm{exp}(-\\lambda(m_i, s_j))) + (1 - X(m_i, s_j)) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (\\mathrm{exp}(-\\lambda(m_i, s_j)))]$$\n",
+    "\n",
+    "\n",
+    "\n",
     "<b> Forecast uncertainty </b> \n",
     "\n",
     "A simulation based approach is used to account for uncertainty in the forecast. We simulate realizations of catalogs that are consistent with the forecast to obtain distributions of scores. In the pyCSEP package, as in the original CSEP tests, simulation is carried out using the cumulative probability density of the forecast obtained by ordering the rates in each bin. We shall call $F_{m_is_j}$ the cumulative probability density in cell $(m_i, s_j)$. The simulation approach then works as follows:\n",
@@ -141,6 +168,7 @@
     "* For each forecast bin, draw a random number $z$ from a uniform distribution between 0 and 1\n",
     "* Assign this event to a space-magnitude bin through the inverse cumulative density distribution at this point $F^{-1}_{m_i, s_j}(z)$\n",
     "* Iterate over all simulated events to generate a catalog containing $N_{sim}$ events consistent with the forecast\n",
+    "* In the case of binary tests, simulate catalogs that are consistent with the number of active cells/bins.\n",
     "\n",
     "For each of these tests, we can plot the distribution of likelihoods computed from theses simulated catalogs relative to the observations using the `plots.plot_poisson_consistency_test` function. We also calculate a quantile score to diagnose a particular forecast with repsect. The number of simulations can be supplied to the Poisson consistency test functions using the `num_simulations` argument: for best results we suggest 100,000 simulations to ensure convergence.\n",
     "\n",
@@ -158,7 +186,9 @@
     "\n",
     "Whether a forecast can be said to pass an evaluation depends on the significance level chosen for the testing process. The quantile score explicitly tells us something about the significance of the result: the observation is consistent with the forecast with $100(1-\\gamma)\\%$ confidence (Zechar, 2011). Low $\\gamma$ values demonstrate that the observed likelihood score is less than most of the simulated catalogs. The consistency tests, excluding the N-test, are considered to be one-sided tests: values which are too small are ruled inconsistent with the forecast, but very large values may not necessarily be inconsistent with the forecast and additional testing should be used to further clarify this (Schorlemmer et al, 2007). \n",
     "\n",
-    "Different CSEP experiments have used different sensitivity values. Schorlemmer et al (2010b) consider $\\gamma \\lt 0.05$ while the implementation in the Italian CSEP testing experiment uses $\\gamma$ < 0.01 (Taroni et al, 2018). However, the consistency tests are most useful as diagnostic tools where the quantile score assesses the level of consistency between observations and data. Temporal variations in seismicity make it difficult to formally reject a model from a consistency test over a single evaluation period."
+    "Different CSEP experiments have used different sensitivity values. Schorlemmer et al (2010b) consider $\\gamma \\lt 0.05$ while the implementation in the Italian CSEP testing experiment uses $\\gamma$ < 0.01 (Taroni et al, 2018). However, the consistency tests are most useful as diagnostic tools where the quantile score assesses the level of consistency between observations and data. Temporal variations in seismicity make it difficult to formally reject a model from a consistency test over a single evaluation period. \n",
+    "\n",
+    "Performing multiple tests among samples of the same distribution increases the probability of observing at least one rare events, and consequently, increases the probability of obtaining an apparently statistically significant result (Kato, 2019). Therefore, CSEP has recently included consistency test results at a Bonferroni-adjusted significance level $\\gamma_{B}$ = 0.05 /2 = 0.025 to control the overall type II error rate, that is, the false-positive rate or the \"false-inconsistency\" rate (see Bayona et al., 2022)."
    ]
   },
   {
@@ -187,7 +217,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -222,7 +252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34cf0e89",
+   "id": "missing-frequency",
    "metadata": {
     "tags": []
    },
@@ -248,7 +278,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -290,7 +320,7 @@
     "\n",
     "<b>Aim</b>: The number or N-test is the most conceptually simple test of a forecast: To test whether the number of observed events is consistent with that of the forecast.\n",
     "\n",
-    "<b>Method</b>: The originial N-test was introduced by Schorlemmer et al (2007) and modified by Zechar et al (2010). The observed number of events is given by,\n",
+    "<b>Method</b>: The original N-test was introduced by Schorlemmer et al (2007) and modified by Zechar et al (2010). The observed number of events is given by,\n",
     "\n",
     "$$N_{obs} = \\sum_{m_i, s_j \\in R} \\omega(m_i, s_j).$$\n",
     "\n",
@@ -338,7 +368,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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Len2NmWRsi4oBpe0myXLg4cAFrei1STYl+chC3a3SdqlsBH4CfLmqLgD2raqrYQho4O7z2MVtMsm4YOGvsxOBvwFuHSlb8OurOZFfHxss/HV2GwNK20WSPYFPA0dW1Q3A+4H7AyuAq4F3z1/vtl1Vba2qFcC9gEcmeeg8d2lOTDKuBb3OkjwD+ElVbZjvvsy1Kca2oNfZeAaU5lw7jvFp4PSq+gxAVf24fQjeCpwEPHI++3hHVdX1wLkMx2l+3I69jR2D+8n89eyOGR3XIlhnjwWemeQq4BPAE5J8nMWxviYc2yJYZ7djQGlOtQPuHwauqKr3jJTvN1LtOcBlO7pvd1SSuyW5c5teCjwJ+C/gC8BhrdphwOfnpYPbaLJxLfR1VlVvqap7VdVy4IXA2VV1KAt8fcHkY1vo62y8nee7A1p0Hgv8ObC5HdMAOBp4UZIVDAffrwJeMR+du4P2A05LsoThy92ZVfWlJOcDZyZ5KfB94OD57OQ2mGxcH1sE62wix7Gw19dU3rmY1pmnmUuSuuQuPklSlwwoSVKXDChJUpcMKElSlwwoSVKXDCipQ0kqybtHnh/VLgQ6F22fmmT1XLQ1zXIOble1P2d7L2uCZR+eZP8dvVzNLQNK6tPNwHOTLJvvjoxqv5WaqZcCr66qx2+v/kzhcMCAWuAMKKlPtwAfAt4w/oXxW0BJtrS/q5J8NcmZSb6d5Lgkh7R7PW1Ocv+RZp6U5Gut3jPa/EuSnJDkonax0VeMtHtOkjOAzRP050Wt/cuSHN/KjgUeB3wgyQkTzPPXI8sZu//U8UlePVJnbZI3TlF/edtCOynDfazWJVna3puVwOkZ7om0tL0X32zzL4pbUfxGqCofPnx09gC2AHdiuBrA3sBRwNr22qnA6tG67e8q4HqGK0PsCvwQeGt77QjgxJH5/4PhC+oBwA+A3YCXA8e0OrsC64H7tnZ/Dtx3gn7uz3A1hrsxXJnmbODZ7bVzgZUTzPNkhvBN68OXgD9kuPL9V0fqfRP47SnqL2cI8hWt/pnAoeOXDewDfItfXZjgzvO9fn3M7OEWlNSpGq4C/1Hg9bOY7aIa7sl1M/DfwLpWvpnhA33MmVV1a1V9B/gu8CCGIHhxu0TVBcBdGQIM4MKqunKC5T0COLeqrq2qW4DTGcJjKk9uj0uAi9uyD6iqS4C7J9k/ycOA/62q709Wv7V1ZVVtbNMbxo1xzA3AL4CTkzwXuHGa/qkTXotP6tuJDB/Kp4yU3ULbPd8uzvtbI6/dPDJ968jzW7n9//fx1zgrhi2U11XVWaMvJFnFsAU1kUzT/8nmeUdVfXCC1z4FrAbuwXCV7knrt/uNjY53K7B0fINVdUuSRwJPZLiw6muBJ2xDv7WDuQUldayqfsqw6+qlI8VXAQe16Wcx3AF3tg5OslM7LnU/hl1gZwGvardLIckDk+wxTTsXAH+UZFk7geJFwFenmecs4CXtnmEkuWeSsZsGfoIhRFYzhNV09SfzM2CvVn9PYO+q+jfgSIZ7JWkBcAtK6t+7Gb71jzkJ+HySC4GvMPnWzVS+xRAk+wKvrKpfJDmZYRfZxW3L7FqmuR16VV2d5C3AOQxbOv9WVVPevqKq1iV5MHD+sBi2AIcy3IDv8iR7AT+sX931drL6W6dYzKkMJ2jcBDyV4f3arfXx1048UZ+8mrkkqUvu4pMkdcmAkiR1yYCSJHXJgJIkdcmAkiR1yYCSJHXJgJIkden/AfCEdh3W3Aw6AAAAAElFTkSuQmCC\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -416,7 +446,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -499,7 +529,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -987,6 +1017,10 @@
    "metadata": {},
    "source": [
     "### References\n",
+    "\n",
+    "Bayona, J.A., Savran, W.H., Rhoades, D.A. and Werner, M.J., 2022. Prospective evaluation of multiplicative hybrid earthquake forecasting models in California. Geophysical Journal International, 229(3), pp.1736-1753.\n",
+    "doi: https://doi.org/10.1093/gji/ggac018\n",
+    "\n",
     "Field, E. H., K. R. Milner, J. L. Hardebeck, M. T. Page, N. J. van der Elst, T. H. Jordan, A. J. Michael, B. E. Shaw, and M. J. Werner (2017). A spatiotemporal clustering model for the third Uniform California Earthquake Rupture Forecast (UCERF3-ETAS): Toward an operational earthquake forecast, Bull. Seismol. Soc. Am. 107, 1049–1081.\n",
     "\n",
     "Harte, D., and D. Vere-Jones (2005), The entropy score and its uses in earthquake forecasting, Pure Appl. Geophys. 162 , 6-7, 1229-1253, DOI: 10.1007/\n",
@@ -1000,6 +1034,16 @@
     "Imoto, M., and D.A. Rhoades (2010), Seismicity models of moderate earthquakes in Kanto, Japan utilizing multiple predictive parameters, Pure Appl. Geophys.\n",
     "167, 6-7, 831-843, DOI: 10.1007/s00024-010-0066-4.\n",
     "\n",
+    "Kato, M., 2019. On the apparently inappropriate use of multiple hypothesis testing in earthquake prediction studies. Seismological Research Letters, 90(3), pp.1330-1334. doi: \n",
+    "https://doi.org/10.1785/0220180378\n",
+    "\n",
+    "\n",
+    "Lombardi, A.M. and Marzocchi, W., 2010. The assumption of Poisson seismic-rate variability in CSEP/RELM experiments. Bulletin of the Seismological Society of America, 100(5A), pp.2293-2300, doi: \n",
+    "https://doi.org/10.1785/0120100012\n",
+    "\n",
+    "Nandan, S., Ouillon, G., Sornette, D. and Wiemer, S., 2019. Forecasting the full distribution of earthquake numbers is fair, robust, and better. Seismological Research Letters, 90(4), pp.1650-1659. doi: \n",
+    "https://doi.org/10.1785/0220180374\n",
+    "\n",
     "Rhoades, D.A, D., Schorlemmer, M.C.Gerstenberger, A. Christophersen, J. D. Zechar & M. Imoto (2011) Efficient testing of earthquake forecasting models, Acta Geophysica 59\n",
     "\n",
     "Savran, W., M. J. Werner, W. Marzocchi, D. Rhoades, D. D. Jackson, K. R. Milner, E. H. Field, and A. J. Michael (2020). Pseudoprospective evaluation of UCERF3-ETAS forecasts during the 2019 Ridgecrest Sequence, Bulletin of the Seismological Society of America.\n",
@@ -1014,8 +1058,12 @@
     "\n",
     "M. Taroni, W. Marzocchi, D. Schorlemmer, M. J. Werner, S. Wiemer, J. D. Zechar, L. Heiniger, F. Euchner; Prospective CSEP Evaluation of 1‐Day, 3‐Month, and 5‐Yr Earthquake Forecasts for Italy. Seismological Research Letters 2018;; 89 (4): 1251–1261. doi: https://doi.org/10.1785/0220180031\n",
     "\n",
+    "\n",
     "Werner, M. J., A. Helmstetter, D. D. Jackson, and Y. Y. Kagan (2011a). High-Resolution Long-Term and Short-Term Earthquake Forecasts for California, Bulletin of the Seismological Society of America 101 1630-1648\n",
     "\n",
+    "Werner, M.J. and Sornette, D., 2008. Magnitude uncertainties impact seismic rate estimates, forecasts, and predictability experiments. Journal of Geophysical Research: Solid Earth, 113(B8). doi: https://doi.org/10.1029/2007JB005427\n",
+    "\n",
+    "\n",
     "Werner, M.J. J.D. Zechar, W. Marzocchi, and S. Wiemer (2011b), Retrospective evaluation of the five-year and ten-year CSEP-Italy earthquake forecasts, Annals of Geophysics 53, no. 3, 11–30, doi:10.4401/ag-4840.\n",
     "\n",
     "Zechar, 2011: Evaluating earthquake predictions and earthquake forecasts: a guide for students and new researchers, CORSSA (http://www.corssa.org/en/articles/theme_6/)\n",
@@ -1025,6 +1073,14 @@
     "Zechar, J.D., D. Schorlemmer, M. Liukis, J. Yu, F. Euchner, P.J. Maechling, and T.H. Jordan (2010b), The Collaboratory for the Study of Earthquake Predictability perspective on computational earthquake science, Concurr. Comp-Pract. E., doi:10.1002/cpe.1519.\n",
     "\n"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fifty-wright",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -1043,7 +1099,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.8"
+   "version": "3.8.6"
   }
  },
  "nbformat": 4,

From 8678a736e952aff626cc64931601c817abc67b55 Mon Sep 17 00:00:00 2001
From: wsavran <35315438+wsavran@users.noreply.github.com>
Date: Thu, 10 Feb 2022 09:11:14 -0800
Subject: [PATCH 13/29] Update setup.py

---
 setup.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/setup.py b/setup.py
index f11037a0..2a4a26ad 100644
--- a/setup.py
+++ b/setup.py
@@ -26,7 +26,7 @@ def get_version():
     long_description=long_description,
     long_description_content_type='text/markdown',
     install_requires = [
-        'numpy',
+        'numpy<=1.21.5',
         'scipy',
         'pandas',
         'matplotlib',

From 9cf5e0e2b70ae910e94bde7c35751c73b861dfd1 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 07:56:26 -0700
Subject: [PATCH 14/29] unpinned numpy version for security issues

---
 requirements.txt | 2 +-
 requirements.yml | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/requirements.txt b/requirements.txt
index 78dfc73b..6a95af5b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,4 +1,4 @@
-numpy<=1.21.5
+numpy
 scipy
 pandas
 matplotlib
diff --git a/requirements.yml b/requirements.yml
index 85779ee0..14caee7e 100644
--- a/requirements.yml
+++ b/requirements.yml
@@ -4,7 +4,7 @@ channels:
   - defaults
 dependencies:
   - python>=3.7
-  - numpy<=1.21.5
+  - numpy
   - pandas
   - scipy
   - matplotlib

From ddca684b567feb5df54c76788af6e5ced2529958 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 10:52:27 -0700
Subject: [PATCH 15/29] added docstrings to plot_pvalues_and_intervals added
 proper imports for plot_pvalues_and_intervals minor code formatting fixed
 issue incorrect percentile in plot_pvalues_and_intervals

---
 csep/utils/plots.py | 168 ++++++++++++++++++++++----------------------
 1 file changed, 85 insertions(+), 83 deletions(-)

diff --git a/csep/utils/plots.py b/csep/utils/plots.py
index ca75fa0d..3c594805 100644
--- a/csep/utils/plots.py
+++ b/csep/utils/plots.py
@@ -6,6 +6,7 @@
 
 import scipy.stats
 import matplotlib
+import matplotlib.lines
 from matplotlib import cm
 from matplotlib.collections import PatchCollection
 import matplotlib.pyplot as pyplot
@@ -1512,6 +1513,7 @@ def plot_comparison_test(results_t, results_w=None, axes=None, plot_args=None):
 
     return ax
 
+
 def plot_poisson_consistency_test(eval_results, normalize=False, one_sided_lower=False, axes=None, plot_args=None, show=False):
     """ Plots results from CSEP1 tests following the CSEP1 convention.
 
@@ -1883,7 +1885,8 @@ def add_labels_for_publication(figure, style='bssa', labelsize=16):
             ax.annotate(f'({annot})', (0.025, 1.025), xycoords='axes fraction', fontsize=labelsize)
 
     return
-    
+
+
 def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, plot_args=None, variance=None):
     """ Plots results from CSEP1 tests following the CSEP1 convention.
 
@@ -1891,7 +1894,7 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
           comparable on the same figure.
 
     Args:
-        results (list): Contains the tests results :class:`csep.core.evaluations.EvaluationResult` (see note above)
+        eval_results (list): Contains the tests results :class:`csep.core.evaluations.EvaluationResult` (see note above)
         normalize (bool): select this if the forecast likelihood should be normalized by the observed likelihood. useful
                           for plotting simulation based simulation tests.
         one_sided_lower (bool): select this if the plot should be for a one sided test
@@ -1936,7 +1939,7 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
     tight_layout = plot_args.get('tight_layout', True)
     percentile = plot_args.get('percentile', 95)
 
-    fig, ax = plt.subplots(figsize=figsize)
+    fig, ax = pyplot.subplots(figsize=figsize)
     xlims = []
     
     for index, res in enumerate(results):
@@ -1952,8 +1955,8 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
             mean = res.test_distribution[1]
             upsilon = 1.0 - ((var - mean) / var)
             tau = (mean**2 /(var - mean))
-            phigh = nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
-            plow = nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
+            phigh = scipy.stats.nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
+            plow = scipy.stats.nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
 
         # empirical distributions
         else:
@@ -2013,118 +2016,117 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
     return ax
     
 
-def plot_pvalues_and_intervals(test_results, var=None):
+def plot_pvalues_and_intervals(test_results, ax, var=None):
+    """ Plots p-values and intervals for a list of Poisson or NBD test results
+
+    Args:
+        test_results (list): list of EvaluationResults for N-test. All tests should use the same distribution
+                             (ie Poisson or NBD).
+        ax (matplotlib.axes.Axes.axis): axes to use for plot. create using matplotlib
+        var (float): variance of the NBD distribution. Must be used for NBD plots.
+
+    Returns:
+        ax (matplotlib.axes.Axes.axis): axes handle containing this plot
+
+    Raises:
+        ValueError: throws error if NBD tests are supplied without a variance
+    """
     
-    variance= var
+    variance = var
     percentile = 97.5
     p_values = []
-    
+
+    # Differentiate between N-tests and other consistency tests
     if test_results[0].name == 'NBD N-Test' or test_results[0].name == 'Poisson N-Test':
-        legend_elements = [Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.0125', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.0125 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
-                           Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.025', markersize=10, markeredgecolor='k')]
-        
+        legend_elements = [matplotlib.lines.Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.0125', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.0125 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
+                           matplotlib.lines.Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.025', markersize=10, markeredgecolor='k')]
         ax.legend(handles=legend_elements, loc=4, fontsize=13, edgecolor='k')
-        
+        # Act on Negative binomial tests
         if test_results[0].name == 'NBD N-Test':
-            
+            if var is None:
+                raise ValueError("var must not be None if N-tests use the NBD distribution.")
+
             for i in range(len(test_results)):
                 mean = test_results[i].test_distribution[1]
                 upsilon = 1.0 - ((variance - mean) / variance)
                 tau = (mean**2 /(variance - mean))
-                phigh97 = nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
-                plow97= nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
+                phigh97 = scipy.stats.nbinom.ppf((1 - percentile/100.)/2., tau, upsilon)
+                plow97 = scipy.stats.nbinom.ppf(1 - (1 - percentile/100.)/2., tau, upsilon)
                 low97 = test_results[i].observed_statistic - plow97
                 high97 = phigh97 - test_results[i].observed_statistic
                 ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) - i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
                             color='slategray', alpha=1.0, zorder=0)
                 p_values.append(test_results[i].quantile[1] * 2.0) # Calculated p-values according to Meletti et al., (2021)
                 
-            if p_values[i] < 10e-5:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
-    
-            if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 0.0125 and p_values[i] < 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
-    
-            if p_values[i] >= 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)
-            
+                if p_values[i] < 10e-5:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='red', markersize=8, zorder=2)
+                if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='#FF7F50', markersize=8, zorder=2)
+                if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='gold', markersize=8, zorder=2)
+                if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='white', markersize=8, zorder=2)
+                if p_values[i] >= 0.0125 and p_values[i] < 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='skyblue', markersize=8, zorder=2)
+                if p_values[i] >= 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='blue', markersize=8, zorder=2)
+        # Act on Poisson N-test
         if test_results[0].name == 'Poisson N-Test':
-            
             for i in range(len(test_results)):
                 plow97 = scipy.stats.poisson.ppf((1 - percentile/100.)/2., test_results[i].test_distribution[1])
-                phigh97 = scipy.stats.poisson.ppf(1- (1 - percentile/100.)/2., test_results[i].test_distribution[1])
+                phigh97 = scipy.stats.poisson.ppf(1 - (1 - percentile/100.)/2., test_results[i].test_distribution[1])
                 low97 = test_results[i].observed_statistic - plow97
                 high97 = phigh97 - test_results[i].observed_statistic
                 ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) - i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
                             color='slategray', alpha=1.0, zorder=0)
                 p_values.append(test_results[i].quantile[1] * 2.0)
-                        
-            if p_values[i] < 10e-5:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
-    
-            if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 10e-3 and p_values[i] < 0.0125:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
-        
-            if p_values[i] >= 0.0125 and p_values[i] < 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
-    
-            if p_values[i] >= 0.025:
-                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)
-    
-    
+                if p_values[i] < 10e-5:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='red', markersize=8, zorder=2)
+                elif p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='#FF7F50', markersize=8, zorder=2)
+                elif p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='gold', markersize=8, zorder=2)
+                elif p_values[i] >= 10e-3 and p_values[i] < 0.0125:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='white', markersize=8, zorder=2)
+                elif p_values[i] >= 0.0125 and p_values[i] < 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='skyblue', markersize=8, zorder=2)
+                elif p_values[i] >= 0.025:
+                    ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='blue', markersize=8, zorder=2)
+    # Operate on all other consistency tests
     else:
         for i in range(len(test_results)):
             plow97 = numpy.percentile(test_results[i].test_distribution, 2.5)
-            phigh97 = numpy.percentile(test_results[i].test_distribution, 100)
+            phigh97 = numpy.percentile(test_results[i].test_distribution, 97.5)
             low97 = test_results[i].observed_statistic - plow97
             high97 = phigh97 - test_results[i].observed_statistic  
             ax.errorbar(test_results[i].observed_statistic, (len(test_results)-1) -i, xerr=numpy.array([[low97, high97]]).T, capsize=4, 
                         color='slategray', alpha=1.0, zorder=0)
             p_values.append(test_results[i].quantile)
 
-        if p_values[i] < 10e-5:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'red', markersize= 8, zorder=2)
-    
-        if p_values[i] >= 10e-5 and p_values[i] < 10e-4:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = '#FF7F50', markersize= 8, zorder=2)
-        
-        if p_values[i] >= 10e-4 and p_values[i] < 10e-3:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'gold', markersize= 8, zorder=2)
-        
-        if p_values[i] >= 10e-3  and p_values[i] < 0.025:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'white', markersize= 8, zorder=2)
-        
-        if p_values[i] >= 0.025 and p_values[i] < 0.05:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'skyblue', markersize= 8, zorder=2)    
-    
-        if p_values[i] >= 0.05:
-            ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color = 'blue', markersize= 8, zorder=2)  
+            if p_values[i] < 10e-5:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='red', markersize=8, zorder=2)
+            elif p_values[i] >= 10e-5 and p_values[i] < 10e-4:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='#FF7F50', markersize=8, zorder=2)
+            elif p_values[i] >= 10e-4 and p_values[i] < 10e-3:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='gold', markersize=8, zorder=2)
+            elif p_values[i] >= 10e-3  and p_values[i] < 0.025:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='white', markersize=8, zorder=2)
+            elif p_values[i] >= 0.025 and p_values[i] < 0.05:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='skyblue', markersize=8, zorder=2)
+            elif p_values[i] >= 0.05:
+                ax.plot(test_results[i].observed_statistic, (len(test_results)-1) - i, marker='o', color='blue', markersize=8, zorder=2)
     
-        legend_elements = [Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.025 $\leq$ p < 0.05', markersize=10, markeredgecolor='k'),
-                   Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.05', markersize=10, markeredgecolor='k')]
+        legend_elements = [
+            matplotlib.lines.Line2D([0], [0], marker='o', color='red', lw=0, label=r'p < 10e-5', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='#FF7F50', lw=0, label=r'10e-5 $\leq$ p < 10e-4', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='gold', lw=0, label=r'10e-4 $\leq$ p < 10e-3', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='white', lw=0, label=r'10e-3 $\leq$ p < 0.025', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='skyblue', lw=0, label=r'0.025 $\leq$ p < 0.05', markersize=10, markeredgecolor='k'),
+            matplotlib.lines.Line2D([0], [0], marker='o', color='blue', lw=0, label=r'p $\geq$ 0.05', markersize=10, markeredgecolor='k')]
 
         ax.legend(handles=legend_elements, loc=4, fontsize=13, edgecolor='k') 
     

From f7ad4194c9f87dc1b96db5ae3160e30afb77a017 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 10:54:51 -0700
Subject: [PATCH 16/29] fixed failing test with python 3.10 due to floating
 point rounding issue

---
 tests/test_csep1_evaluations.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/tests/test_csep1_evaluations.py b/tests/test_csep1_evaluations.py
index a733003f..b870ef6a 100644
--- a/tests/test_csep1_evaluations.py
+++ b/tests/test_csep1_evaluations.py
@@ -125,9 +125,9 @@ def test_t_test(self):
                            'information_gain': 0.08052612477654024,
                            'ig_lower': -0.029435677283374914,
                            'ig_upper': 0.19048792683645538}
-
-        print('T Test: Running Unit Test')
-        self.assertEqual(_t_test_ndarray(forecast_A, forecast_B, numpy.sum(obs), forecast_A.sum(), forecast_B.sum()), t_test_expected, 'Failed T Test')
+        numpy.testing.assert_allclose(
+            _t_test_ndarray(forecast_A, forecast_B, numpy.sum(obs), forecast_A.sum(), forecast_B.sum()),
+            t_test_expected)
 
 
 if __name__ == '__main__':

From 0ef85ed2ee98fb2b65d60622b268a3150b2b1ec1 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 26 Jul 2022 11:22:10 -0700
Subject: [PATCH 17/29] fixed warnings from numpy np.int -> np.int64 minor code
 formatting updates update tests for python 3.10: failing absolute assertion
 changing to numpy.testing.all_close in csep1 t-test

---
 csep/core/regions.py            |  4 ++--
 csep/utils/basic_types.py       |  2 +-
 csep/utils/calc.py              | 14 +++++++-------
 tests/test_csep1_evaluations.py | 23 ++++++++++++-----------
 4 files changed, 22 insertions(+), 21 deletions(-)

diff --git a/csep/core/regions.py b/csep/core/regions.py
index e9551f03..04795c01 100644
--- a/csep/core/regions.py
+++ b/csep/core/regions.py
@@ -631,14 +631,14 @@ def get_index_of(self, lons, lats):
             raise ValueError("at least one lon and lat pair contain values that are outside of the valid region.")
         if numpy.any(self.bbox_mask[idy, idx] == 1):
             raise ValueError("at least one lon and lat pair contain values that are outside of the valid region.")
-        return self.idx_map[idy,idx].astype(numpy.int)
+        return self.idx_map[idy, idx].astype(numpy.int64)
 
     def get_location_of(self, indices):
         """
         Returns the polygon associated with the index idx.
 
         Args:
-            idx: index of polygon in region
+            indices: index of polygon in region
 
         Returns:
             Polygon
diff --git a/csep/utils/basic_types.py b/csep/utils/basic_types.py
index 5e1f5aa5..c8c5168e 100644
--- a/csep/utils/basic_types.py
+++ b/csep/utils/basic_types.py
@@ -51,7 +51,7 @@ def add(self, data):
 
         # need to know the range of the data to be inserted on discretized grid (min, max)
         # this is to determine the discretization of the data
-        eps=np.finfo(np.float).eps
+        eps = np.finfo(np.float64).eps
         disc_min = np.floor((data_min+eps-self.anchor)*self.rec_dh)/self.rec_dh+self.anchor
         disc_max = np.ceil((data_max+eps-self.anchor)*self.rec_dh)/self.rec_dh+self.anchor
 
diff --git a/csep/utils/calc.py b/csep/utils/calc.py
index e0071f47..dc208cda 100644
--- a/csep/utils/calc.py
+++ b/csep/utils/calc.py
@@ -79,9 +79,9 @@ def bin1d_vec(p, bins, tol=None, right_continuous=False):
     else:
         h = bins[1] - bins[0]
 
-    a0_tol = numpy.abs(a0) * numpy.finfo(numpy.float).eps
-    h_tol = numpy.abs(h) * numpy.finfo(numpy.float).eps
-    p_tol = numpy.abs(p) * numpy.finfo(numpy.float).eps
+    a0_tol = numpy.abs(a0) * numpy.finfo(numpy.float64).eps
+    h_tol = numpy.abs(h) * numpy.finfo(numpy.float64).eps
+    p_tol = numpy.abs(p) * numpy.finfo(numpy.float64).eps
 
     # absolute tolerance
     if tol is None:
@@ -97,7 +97,7 @@ def bin1d_vec(p, bins, tol=None, right_continuous=False):
         try:
             idx[(idx < 0)] = -1
             idx[(idx >= len(bins) - 1)] = len(bins) - 1
-        except (TypeError):
+        except TypeError:
             if idx >= len(bins) - 1:
                 idx = len(bins) - 1
             if idx < 0:
@@ -105,12 +105,12 @@ def bin1d_vec(p, bins, tol=None, right_continuous=False):
     else:
         try:
             idx[((idx < 0) | (idx >= len(bins)))] = -1
-        except (TypeError):
+        except TypeError:
             if idx < 0 or idx >= len(bins):
                 idx = -1
     try:
-        idx = idx.astype(numpy.int)
-    except (AttributeError):
+        idx = idx.astype(numpy.int64)
+    except AttributeError:
         idx = int(idx)
     return idx
 
diff --git a/tests/test_csep1_evaluations.py b/tests/test_csep1_evaluations.py
index b870ef6a..d095e677 100644
--- a/tests/test_csep1_evaluations.py
+++ b/tests/test_csep1_evaluations.py
@@ -21,6 +21,7 @@ def get_datadir():
     data_dir = os.path.join(root_dir, 'artifacts', 'example_csep1_forecasts')
     return data_dir
 
+
 class TestCSEP1NTestThreeMonthsEEPAS(unittest.TestCase):
 
     def __init__(self, *args, **kwargs):
@@ -61,8 +62,8 @@ def test_ntest_three_months_eepas_model(self):
         test_evaluation_dict['event_count_forecast'] = fore.event_count
         test_evaluation_dict['event_count'] = cata.event_count
         # comparing floats, so we will just map to ndarray and use allclose
-        expected = numpy.array([v for k,v in result_dict.items()])
-        computed = numpy.array([v for k,v in test_evaluation_dict.items()])
+        expected = numpy.array([v for k, v in result_dict.items()])
+        computed = numpy.array([v for k, v in test_evaluation_dict.items()])
         numpy.testing.assert_allclose(expected, computed, rtol=1e-5)
 
 
@@ -82,13 +83,13 @@ def _parse_xml_result(self):
             xml_result['event_count'] = float(child.find('ns0:eventCount', ns).text)
         return xml_result
 
-class TestGriddedForecastTests(unittest.TestCase):
 
+class TestGriddedForecastTests(unittest.TestCase):
 
     def test_n_test(self):
-        forecast = numpy.zeros((10,10))+0.0015
+        forecast = numpy.zeros((10, 10))+0.0015
         forecast = forecast / forecast.size
-        observation = numpy.zeros((10,10))
+        observation = numpy.zeros((10, 10))
         expected_output = (1.0, 0.9985011244377109)
         print('N Test: Running Unit Test')
         numpy.testing.assert_allclose(_number_test_ndarray(forecast.sum(), observation.sum()), expected_output)
@@ -116,18 +117,18 @@ def test_t_test(self):
         the equations from
 
         """
-        forecast_A = numpy.array([[8, 2], [3, 5]])
-        forecast_B = numpy.array([[6, 4], [2, 8]])
+        forecast_a = numpy.array([[8, 2], [3, 5]])
+        forecast_b = numpy.array([[6, 4], [2, 8]])
         obs = numpy.array([[5, 8], [4, 2]])
 
-        t_test_expected = {'t_critical': 2.10092204024096,
-                           't_statistic': 1.5385261717159382,
+        t_test_expected = {'t_statistic': 1.5385261717159382,
+                           't_critical': 2.10092204024096,
                            'information_gain': 0.08052612477654024,
                            'ig_lower': -0.029435677283374914,
                            'ig_upper': 0.19048792683645538}
         numpy.testing.assert_allclose(
-            _t_test_ndarray(forecast_A, forecast_B, numpy.sum(obs), forecast_A.sum(), forecast_B.sum()),
-            t_test_expected)
+            [v for k, v in _t_test_ndarray(forecast_a, forecast_b, numpy.sum(obs), forecast_a.sum(), forecast_b.sum()).items()],
+            [v for k, v in t_test_expected.items()])
 
 
 if __name__ == '__main__':

From d6ea660d2fbfa24ca2e743f31cc1110946ba2ceb Mon Sep 17 00:00:00 2001
From: bayonato89 <72937672+bayonato89@users.noreply.github.com>
Date: Thu, 18 Aug 2022 19:01:51 +0100
Subject: [PATCH 18/29] Non poissonian tests (#189)

* Changed np for numpy in the poisson_evaluations.py file
* Added non-Poissonian comparative and consistency tests.
* format  docstrings
* Rename non_poissonian_evaluations.py to binomial_evaluations.py
* Update binomial_evaluations.py
removed unused imports

Co-authored-by: wsavran <35315438+wsavran@users.noreply.github.com>
---
 csep/core/binomial_evaluations.py | 372 ++++++++++++++++++++++++++++++
 1 file changed, 372 insertions(+)
 create mode 100644 csep/core/binomial_evaluations.py

diff --git a/csep/core/binomial_evaluations.py b/csep/core/binomial_evaluations.py
new file mode 100644
index 00000000..9ecd61ea
--- /dev/null
+++ b/csep/core/binomial_evaluations.py
@@ -0,0 +1,372 @@
+import numpy
+import scipy.stats
+import scipy.spatial
+
+from csep.models import EvaluationResult
+from csep.core.exceptions import CSEPCatalogException
+
+def _nbd_number_test_ndarray(fore_cnt, obs_cnt, variance, epsilon=1e-6):
+    """ Computes delta1 and delta2 values from the Negative Binomial (NBD) number test.
+
+    Args:
+        fore_cnt (float): parameter of negative binomial distribution coming from expected value of the forecast
+        obs_cnt (float): count of earthquakes observed during the testing period.
+        variance (float): variance parameter of negative binomial distribution coming from historical catalog. 
+        A variance value of approximately 23541 has been calculated using M5.95+ earthquakes observed worldwide from 1982 to 2013.
+        epsilon (float): tolerance level to satisfy the requirements of two-sided p-value
+
+    Returns
+        result (tuple): (delta1, delta2)
+    """
+    var = variance
+    mean = fore_cnt
+    upsilon = 1.0 - ((var - mean) / var)
+    tau = (mean**2 /(var - mean))
+    
+    delta1 = 1.0 - scipy.stats.nbinom.cdf(obs_cnt - epsilon, tau, upsilon, loc=0)
+    delta2 = scipy.stats.nbinom.cdf(obs_cnt + epsilon, tau, upsilon, loc=0)
+
+    return delta1, delta2
+
+    
+def negative_binomial_number_test(gridded_forecast, observed_catalog, variance):
+    """ Computes "negative binomial N-Test" on a gridded forecast.
+
+    Computes Number (N) test for Observed and Forecasts. Both data sets are expected to be in terms of event counts.
+    We find the Total number of events in Observed Catalog and Forecasted Catalogs. Which are then employed to compute the 
+    probablities of
+    (i) At least no. of events (delta 1)
+    (ii) At most no. of events (delta 2) assuming the negative binomial distribution.
+
+    Args:
+        gridded_forecast:   Forecast of a Model (Gridded) (Numpy Array)
+                    A forecast has to be in terms of Average Number of Events in Each Bin
+                    It can be anything greater than zero
+        observed_catalog:   Observed (Gridded) seismicity (Numpy Array):
+                    An Observation has to be Number of Events in Each Bin
+                    It has to be a either zero or positive integer only (No Floating Point)
+        variance:   Variance parameter of negative binomial distribution obtained from historical catalog.            
+
+    Returns:
+        out (tuple): (delta_1, delta_2)
+    """
+    result = EvaluationResult()
+
+    # observed count
+    obs_cnt = observed_catalog.event_count
+
+    # forecasts provide the expeceted number of events during the time horizon of the forecast
+    fore_cnt = gridded_forecast.event_count
+
+    epsilon = 1e-6
+
+    # stores the actual result of the number test
+    delta1, delta2 = _nbd_number_test_ndarray(fore_cnt, obs_cnt, variance, epsilon=epsilon)
+    
+    # store results
+    result.test_distribution = ('negative_binomial', fore_cnt)
+    result.name = 'NBD N-Test'
+    result.observed_statistic = obs_cnt
+    result.quantile = (delta1, delta2)
+    result.sim_name = gridded_forecast.name
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    result.min_mw = numpy.min(gridded_forecast.magnitudes)
+
+    return result
+  
+    
+def binary_joint_log_likelihood_ndarray(forecast, catalog):
+    """ Computes Bernoulli log-likelihood scores, assuming that earthquakes follow a binomial distribution.
+    
+    Args:
+        forecast:   Forecast of a Model (Gridded) (Numpy Array)
+                    A forecast has to be in terms of Average Number of Events in Each Bin
+                    It can be anything greater than zero
+        catalog:    Observed (Gridded) seismicity (Numpy Array):
+                    An Observation has to be Number of Events in Each Bin
+                    It has to be a either zero or positive integer only (No Floating Point)
+    """
+    #First, we mask the forecast in cells where we could find log=0.0 singularities:
+    forecast_masked = np.ma.masked_where(forecast.ravel() <= 0.0, forecast.ravel()) 
+    
+    #Then, we compute the log-likelihood of observing one or more events given a Poisson distribution, i.e., 1 - Pr(0) 
+    target_idx = numpy.nonzero(catalog.ravel())
+    y = numpy.zeros(forecast_masked.ravel().shape)
+    y[target_idx[0]] = 1
+    first_term = y * (np.log(1.0 - np.exp(-forecast_masked.ravel())))
+    
+    #Also, we estimate the log-likelihood in cells no events are observed:
+    second_term = (1-y) * (-forecast_masked.ravel().data)
+    #Finally, we sum both terms to compute the joint log-likelihood score:
+    return sum(first_term.data + second_term.data)
+    
+    
+def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000, random_numbers=None, 
+                              seed=None, use_observed_counts=True, verbose=True, normalize_likelihood=False):
+    """  Computes binary conditional-likelihood test from CSEP using an efficient simulation based approach.
+    
+    Args:
+        forecast_data (numpy.ndarray): nd array where [:, -1] are the magnitude bins.
+        observed_data (numpy.ndarray): same format as observation.
+        num_simulations: default number of simulations to use for likelihood based simulations
+        seed: used for reproducibility of the prng
+        random_numbers (numpy.ndarray): can supply an explicit list of random numbers, primarily used for software testing
+        use_observed_counts (bool): if true, will simulate catalogs using the observed events, if false will draw from poisson 
+        distribution
+    """
+    
+    # Array-masking that avoids log singularities:
+    forecast_data = numpy.ma.masked_where(forecast_data <= 0.0, forecast_data) 
+    
+    # set seed for the likelihood test
+    if seed is not None:
+        numpy.random.seed(seed)
+
+    # used to determine where simulated earthquake should be placed, by definition of cumsum these are sorted
+    sampling_weights = numpy.cumsum(forecast_data.ravel()) / numpy.sum(forecast_data)
+
+    # data structures to store results
+    sim_fore = numpy.zeros(sampling_weights.shape)
+    simulated_ll = []
+    n_obs = len(np.unique(np.nonzero(observed_data.ravel())))
+    n_fore = numpy.sum(forecast_data)
+    expected_forecast_count = int(n_obs) 
+    
+    if use_observed_counts and normalize_likelihood:
+        scale = n_obs / n_fore
+        expected_forecast_count = int(n_obs)
+        forecast_data = scale * forecast_data
+
+    # main simulation step in this loop
+    for idx in range(num_simulations):
+        if use_observed_counts:
+            num_events_to_simulate = int(n_obs)
+        else:
+            num_events_to_simulate = int(numpy.random.poisson(expected_forecast_count))
+    
+        if random_numbers is None:
+            sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore)
+        else:
+            sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore,
+                                         random_numbers=random_numbers[idx,:])
+
+    
+        # compute joint log-likelihood
+        current_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, sim_fore)
+        
+        # append to list of simulated log-likelihoods
+        simulated_ll.append(current_ll)
+
+        # just be verbose
+        if verbose:
+            if (idx + 1) % 100 == 0:
+                print(f'... {idx + 1} catalogs simulated.')
+                
+                target_idx = numpy.nonzero(catalog.ravel())
+
+    # observed joint log-likelihood
+    obs_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, observed_data)
+        
+    # quantile score
+    qs = numpy.sum(simulated_ll <= obs_ll) / num_simulations
+
+    # float, float, list
+    return qs, obs_ll, simulated_ll
+ 
+    
+def binary_spatial_test(gridded_forecast, observed_catalog, num_simulations=1000, seed=None, random_numbers=None, verbose=False):
+    """  Performs the binary spatial test on the Forecast using the Observed Catalogs.
+    
+    Note: The forecast and the observations should be scaled to the same time period before calling this function. This increases
+    transparency as no assumptions are being made about the length of the forecasts. This is particularly important for
+    gridded forecasts that supply their forecasts as rates.
+    
+    Args:
+        gridded_forecast: csep.core.forecasts.GriddedForecast
+        observed_catalog: csep.core.catalogs.Catalog
+        num_simulations (int): number of simulations used to compute the quantile score
+        seed (int): used fore reproducibility, and testing
+        random_numbers (numpy.ndarray): random numbers used to override the random number generation. injection point for testing.
+        
+    Returns:
+        evaluation_result: csep.core.evaluations.EvaluationResult
+    """
+
+    # grid catalog onto spatial grid
+    gridded_catalog_data = observed_catalog.spatial_counts()
+
+    # simply call likelihood test on catalog data and forecast
+    qs, obs_ll, simulated_ll = _binary_likelihood_test(gridded_forecast.spatial_counts(), gridded_catalog_data,
+                                                        num_simulations=num_simulations,
+                                                        seed=seed,
+                                                        random_numbers=random_numbers,
+                                                        use_observed_counts=True,
+                                                        verbose=verbose, normalize_likelihood=True)
+
+    
+# populate result data structure
+    result = EvaluationResult()
+    result.test_distribution = simulated_ll
+    result.name = 'Binary S-Test'
+    result.observed_statistic = obs_ll
+    result.quantile = qs
+    result.sim_name = gridded_forecast.name
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    try:
+        result.min_mw = numpy.min(gridded_forecast.magnitudes)
+    except AttributeError:
+        result.min_mw = -1
+    return result
+    
+    
+def binary_conditional_likelihood_test(gridded_forecast, observed_catalog, num_simulations=1000, seed=None, random_numbers=None, verbose=False):
+    """ Performs the binary conditional likelihood test on Gridded Forecast using an Observed Catalog.
+
+    Normalizes the forecast so the forecasted rate are consistent with the observations. This modification
+    eliminates the strong impact differences in the number distribution have on the forecasted rates.
+
+    Note: The forecast and the observations should be scaled to the same time period before calling this function. This increases
+    transparency as no assumptions are being made about the length of the forecasts. This is particularly important for
+    gridded forecasts that supply their forecasts as rates.
+
+    Args:
+        gridded_forecast: csep.core.forecasts.GriddedForecast
+        observed_catalog: csep.core.catalogs.Catalog
+        num_simulations (int): number of simulations used to compute the quantile score
+        seed (int): used fore reproducibility, and testing
+        random_numbers (numpy.ndarray): random numbers used to override the random number generation. injection point for testing.
+
+    Returns:
+        evaluation_result: csep.core.evaluations.EvaluationResult
+    """
+        
+    # grid catalog onto spatial grid
+    try:
+        _ = observed_catalog.region.magnitudes
+    except CSEPCatalogException:
+        observed_catalog.region = gridded_forecast.region
+    gridded_catalog_data = observed_catalog.spatial_magnitude_counts()
+
+    # simply call likelihood test on catalog data and forecast
+    qs, obs_ll, simulated_ll = _binary_likelihood_test(gridded_forecast.data, gridded_catalog_data,
+                                                        num_simulations=num_simulations, seed=seed, random_numbers=random_numbers,
+                                                        use_observed_counts=True,
+                                                        verbose=verbose, normalize_likelihood=False)
+
+    # populate result data structure
+    result = EvaluationResult()
+    result.test_distribution = simulated_ll
+    result.name = 'Binary CL-Test'
+    result.observed_statistic = obs_ll
+    result.quantile = qs
+    result.sim_name = gridded_forecast.name
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    result.min_mw = numpy.min(gridded_forecast.magnitudes)
+
+    return result
+     
+    
+def matrix_binary_t_test(target_event_rates1, target_event_rates2, n_obs, n_f1, n_f2, catalog, alpha=0.05):
+    """ Computes binary T test statistic by comparing two target event rate distributions.
+
+    We compare Forecast from Model 1 and with Forecast of Model 2. Information Gain per Active Bin (IGPA) is computed, which is then 
+    employed to compute T statistic. Confidence interval of Information Gain can be computed using T_critical. For a complete 
+    explanation see Rhoades, D. A., et al., (2011). Efficient testing of earthquake forecasting models. Acta Geophysica, 59(4), 
+    728-747. doi:10.2478/s11600-011-0013-5, and Bayona J.A. et al., (2022). Prospective evaluation of multiplicative hybrid earthquake 
+    forecasting models in California. doi: 10.1093/gji/ggac018.
+    
+    Args:
+        target_event_rates1 (numpy.ndarray): nd-array storing target event rates
+        target_event_rates2 (numpy.ndarray): nd-array storing target event rates
+        n_obs (float, int, numpy.ndarray): number of observed earthquakes, should be whole number and >= zero.
+        n_f1 (float): Total number of forecasted earthquakes by Model 1
+        n_f2 (float): Total number of forecasted earthquakes by Model 2
+        catalog: csep.core.catalogs.Catalog
+        alpha (float): tolerance level for the type-i error rate of the statistical test
+
+    Returns:
+        out (dict): relevant statistics from the t-test
+    """
+    # Some Pre Calculations -  Because they are being used repeatedly.
+    N_p = n_obs  
+    N = len(np.unique(np.nonzero(catalog.spatial_magnitude_counts().ravel()))) # Number of active bins
+    N1 = n_f1  
+    N2 = n_f2  
+    X1 = numpy.log(target_event_rates1)  # Log of every element of Forecast 1
+    X2 = numpy.log(target_event_rates2)  # Log of every element of Forecast 2
+    
+
+    # Information Gain, using Equation (17)  of Rhoades et al. 2011
+    information_gain = (numpy.sum(X1 - X2) - (N1 - N2)) / N
+
+    # Compute variance of (X1-X2) using Equation (18)  of Rhoades et al. 2011
+    first_term = (numpy.sum(numpy.power((X1 - X2), 2))) / (N - 1)
+    second_term = numpy.power(numpy.sum(X1 - X2), 2) / (numpy.power(N, 2) - N)
+    forecast_variance = first_term - second_term
+
+    forecast_std = numpy.sqrt(forecast_variance)
+    t_statistic = information_gain / (forecast_std / numpy.sqrt(N))
+
+    # Obtaining the Critical Value of T from T distribution.
+    df = N - 1
+    t_critical = scipy.stats.t.ppf(1 - (alpha / 2), df)  # Assuming 2-Tail Distribution  for 2 tail, divide 0.05/2.
+
+    # Computing Information Gain Interval.
+    ig_lower = information_gain - (t_critical * forecast_std / numpy.sqrt(N))
+    ig_upper = information_gain + (t_critical * forecast_std / numpy.sqrt(N))
+
+    # If T value greater than T critical, Then both Lower and Upper Confidence Interval limits will be greater than Zero.
+    # If above Happens, Then It means that Forecasting Model 1 is better than Forecasting Model 2.
+    return {'t_statistic': t_statistic,
+            't_critical': t_critical,
+            'information_gain': information_gain,
+            'ig_lower': ig_lower,
+            'ig_upper': ig_upper}
+    
+
+def binary_paired_t_test(forecast, benchmark_forecast, observed_catalog, alpha=0.05, scale=False):
+    """ Computes the binary t-test for gridded earthquake forecasts.
+
+    This score is positively oriented, meaning that positive values of the information gain indicate that the
+    forecast is performing better than the benchmark forecast.
+
+    Args:
+        forecast (csep.core.forecasts.GriddedForecast): nd-array storing gridded rates, axis=-1 should be the magnitude column
+        benchmark_forecast (csep.core.forecasts.GriddedForecast): nd-array storing gridded rates, axis=-1 should be the magnitude 
+        column
+        observed_catalog (csep.core.catalogs.AbstractBaseCatalog): number of observed earthquakes, should be whole number and >= zero.
+        alpha (float): tolerance level for the type-i error rate of the statistical test
+        scale (bool): if true, scale forecasted rates down to a single day
+
+    Returns:
+        evaluation_result: csep.core.evaluations.EvaluationResult
+    """
+
+    # needs some pre-processing to put the forecasts in the context that is required for the t-test. this is different
+    # for cumulative forecasts (eg, multiple time-horizons) and static file-based forecasts.
+    target_event_rate_forecast1p, n_fore1 = forecast.target_event_rates(observed_catalog, scale=scale)
+    target_event_rate_forecast2p, n_fore2 = benchmark_forecast.target_event_rates(observed_catalog, scale=scale)
+    
+    target_event_rate_forecast1 = forecast.data.ravel()[np.unique(np.nonzero(observed_catalog.spatial_magnitude_counts().ravel()))]
+    target_event_rate_forecast2 = benchmark_forecast.data.ravel()[np.unique(np.nonzero(observed_catalog.spatial_magnitude_counts().
+    ravel()))]
+
+    # call the primative version operating on ndarray
+    out = matrix_binary_t_test(target_event_rate_forecast1, target_event_rate_forecast2, observed_catalog.event_count, n_fore1, n_fore2,
+                          observed_catalog,
+                          alpha=alpha)
+
+    # storing this for later
+    result = EvaluationResult()
+    result.name = 'binary paired T-Test'
+    result.test_distribution = (out['ig_lower'], out['ig_upper'])
+    result.observed_statistic = out['information_gain']
+    result.quantile = (out['t_statistic'], out['t_critical'])
+    result.sim_name = (forecast.name, benchmark_forecast.name)
+    result.obs_name = observed_catalog.name
+    result.status = 'normal'
+    result.min_mw = np.min(forecast.magnitudes)
+    return result

From 81b177a2f36e9c8eb0b43a8e481104c8689ec853 Mon Sep 17 00:00:00 2001
From: bayonato89 <72937672+bayonato89@users.noreply.github.com>
Date: Thu, 22 Sep 2022 18:00:40 +0100
Subject: [PATCH 19/29] Notebook documentation (#202)

* Added some documentation on new binary CSEP tests.
---
 notebooks/CSEP_tests.ipynb | 76 +++++++++++++++++++++++++++++++++-----
 1 file changed, 66 insertions(+), 10 deletions(-)

diff --git a/notebooks/CSEP_tests.ipynb b/notebooks/CSEP_tests.ipynb
index da30f86c..b377641c 100644
--- a/notebooks/CSEP_tests.ipynb
+++ b/notebooks/CSEP_tests.ipynb
@@ -72,7 +72,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fetched ComCat catalog in 5.9399449825286865 seconds.\n",
+      "Fetched ComCat catalog in 5.9891064167022705 seconds.\n",
       "\n",
       "Downloaded catalog from ComCat with following parameters\n",
       "Start Date: 2010-01-10 00:27:39.320000+00:00\n",
@@ -134,6 +134,33 @@
     "\n",
     "where $\\lambda(m_i, s_j)$ and $\\omega(m_i, s_j)$ are the expected counts from the forecast and observed counts in cell $m_i, s_j$ respectively. We can calculate the likelihood directly given the forecast and discretised observations.\n",
     "\n",
+    "#### Binary consistency tests\n",
+    "\n",
+    "It is known that the Poisson distribution insufficiently captures the variability of earthquakes, as it could be dispersed with respect to the true distribution of seismicity, especially in the presence of clustered earthquakes (Werner and Sornette, 2008; Lombardi and Marzocchi, 2010; Nandan et al., 2019). Therefore, CSEP has recently introduced a set of new consistency tests based on the negative binomial distribution (NBD) and a binary likelihood function, with the aim of reducing the sensitivity of traditional Poisson-based tests to clustering (Bayona et al., 2022).\n",
+    "\n",
+    "The NBD has been shown to better describe non-declustered seismicity, because it has a greater variance than the Poisson distribution to account for spatiotemporal earthquake clustering (Werner et al., 2011a,b). Hence, one can fit a NBD to the rates of observed earthquakes in each forecast's testing region to evaluate number consistencies between forecasts and observations. The probability mass function of an NBD is defined by:\n",
+    "\n",
+    "$P (\\omega\\hspace{0.1cm}|\\hspace{0.1cm}\\tau, \\nu) = \\frac{\\Gamma(\\tau + \\omega)}{\\Gamma(\\tau)\\omega!} \\nu^\\omega (1-\\nu)^{\\omega},$\n",
+    "\n",
+    "where $\\omega = 0,1,2,...$ is the number of events, $\\tau > 0$ and $0 \\leq \\nu \\leq 1$ are parameters, and $\\Gamma$ is the Gamma function. The mean $\\mu$ and  variance $\\sigma^2$ of the NBD are given by\n",
+    "\n",
+    "$\\mu = \\tau\\frac{1 - \\nu}{\\nu}; \\hspace{0.1cm} \\sigma^2=\\tau \\frac{1 - \\nu}{\\nu^2}$.\n",
+    "\n",
+    "Following the approach by Werner et al. (2011b), one can use the expected number earthquakes by the forecast as the mean and estimate the variance from historical catalogs.\n",
+    "\n",
+    "The binary likelihood function can also make the assumption that earthquakes are Poisson distributed less critical by calculating the probability of observing one or more earthquakes in a forecast cell/bin, rather than the likelihood of observing $\\omega =$ 1,2, .., n events. The probability of observing $\\omega = $ 0 earthquakes given an expected number/rate $\\lambda$, assuming a Poisson distribution, is P$_\\mathrm{0}$ = exp(-$\\lambda)$, while the probability of observing one or more events is P$_\\mathrm{_1}$ = 1 - P$_\\mathrm{0}$ = 1 - exp($-\\lambda)$. Accordingly, one can compute the log-likelihood score in each cell/bin based on the binary (or Bernoulli) distribution as:\n",
+    "\n",
+    "$$ L(\\boldsymbol{\\Omega} | \\boldsymbol{\\Lambda}) = X(m_i, s_j) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} \\mathrm{P_1} + (1 -X(m_i, s_j)) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} \\mathrm{P_0} = X(m_i, s_j) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (1-\\mathrm{exp}(-\\lambda(m_i, s_j))) + (1 -X_i) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (\\mathrm{exp}(-\\lambda(m_i, s_j)))$$\n",
+    "\n",
+    "where the first term represents the contribution to the score if a bin $(m_i, s_j)$ contains one or more events, i.e. $X(m_i, s_j)$ = 1, and the second term is the contribution if that cell/bin contains no earthquakes, i.e. $X(m_i, s_j)$ = 0.\n",
+    "\n",
+    "Similar to the example above, the joint likelihood of observing events in individual bins, based on the binary likelihood function, is the sum of each individual log score, i.e.:\n",
+    "\n",
+    "\n",
+    "$$ L(\\boldsymbol{\\Omega} | \\boldsymbol{\\Lambda})  = \\sum_{m_i , s_j \\in \\boldsymbol{R}} \\hspace{0.05cm}[X(m_i, s_j) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (1-\\mathrm{exp}(-\\lambda(m_i, s_j))) + (1 - X(m_i, s_j)) \\hspace{0.1cm} \\mathrm{log} \\hspace{0.1cm} (\\mathrm{exp}(-\\lambda(m_i, s_j)))]$$\n",
+    "\n",
+    "\n",
+    "\n",
     "<b> Forecast uncertainty </b> \n",
     "\n",
     "A simulation based approach is used to account for uncertainty in the forecast. We simulate realizations of catalogs that are consistent with the forecast to obtain distributions of scores. In the pyCSEP package, as in the original CSEP tests, simulation is carried out using the cumulative probability density of the forecast obtained by ordering the rates in each bin. We shall call $F_{m_is_j}$ the cumulative probability density in cell $(m_i, s_j)$. The simulation approach then works as follows:\n",
@@ -141,6 +168,7 @@
     "* For each forecast bin, draw a random number $z$ from a uniform distribution between 0 and 1\n",
     "* Assign this event to a space-magnitude bin through the inverse cumulative density distribution at this point $F^{-1}_{m_i, s_j}(z)$\n",
     "* Iterate over all simulated events to generate a catalog containing $N_{sim}$ events consistent with the forecast\n",
+    "* In the case of binary tests, simulate catalogs that are consistent with the number of active cells/bins.\n",
     "\n",
     "For each of these tests, we can plot the distribution of likelihoods computed from theses simulated catalogs relative to the observations using the `plots.plot_poisson_consistency_test` function. We also calculate a quantile score to diagnose a particular forecast with repsect. The number of simulations can be supplied to the Poisson consistency test functions using the `num_simulations` argument: for best results we suggest 100,000 simulations to ensure convergence.\n",
     "\n",
@@ -158,7 +186,9 @@
     "\n",
     "Whether a forecast can be said to pass an evaluation depends on the significance level chosen for the testing process. The quantile score explicitly tells us something about the significance of the result: the observation is consistent with the forecast with $100(1-\\gamma)\\%$ confidence (Zechar, 2011). Low $\\gamma$ values demonstrate that the observed likelihood score is less than most of the simulated catalogs. The consistency tests, excluding the N-test, are considered to be one-sided tests: values which are too small are ruled inconsistent with the forecast, but very large values may not necessarily be inconsistent with the forecast and additional testing should be used to further clarify this (Schorlemmer et al, 2007). \n",
     "\n",
-    "Different CSEP experiments have used different sensitivity values. Schorlemmer et al (2010b) consider $\\gamma \\lt 0.05$ while the implementation in the Italian CSEP testing experiment uses $\\gamma$ < 0.01 (Taroni et al, 2018). However, the consistency tests are most useful as diagnostic tools where the quantile score assesses the level of consistency between observations and data. Temporal variations in seismicity make it difficult to formally reject a model from a consistency test over a single evaluation period."
+    "Different CSEP experiments have used different sensitivity values. Schorlemmer et al (2010b) consider $\\gamma \\lt 0.05$ while the implementation in the Italian CSEP testing experiment uses $\\gamma$ < 0.01 (Taroni et al, 2018). However, the consistency tests are most useful as diagnostic tools where the quantile score assesses the level of consistency between observations and data. Temporal variations in seismicity make it difficult to formally reject a model from a consistency test over a single evaluation period. \n",
+    "\n",
+    "Performing multiple tests among samples of the same distribution increases the probability of observing at least one rare events, and consequently, increases the probability of obtaining an apparently statistically significant result (Kato, 2019). Therefore, CSEP has recently included consistency test results at a Bonferroni-adjusted significance level $\\gamma_{B}$ = 0.05 /2 = 0.025 to control the overall type II error rate, that is, the false-positive rate or the \"false-inconsistency\" rate (see Bayona et al., 2022)."
    ]
   },
   {
@@ -187,7 +217,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -222,7 +252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34cf0e89",
+   "id": "missing-frequency",
    "metadata": {
     "tags": []
    },
@@ -248,7 +278,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -290,7 +320,7 @@
     "\n",
     "<b>Aim</b>: The number or N-test is the most conceptually simple test of a forecast: To test whether the number of observed events is consistent with that of the forecast.\n",
     "\n",
-    "<b>Method</b>: The originial N-test was introduced by Schorlemmer et al (2007) and modified by Zechar et al (2010). The observed number of events is given by,\n",
+    "<b>Method</b>: The original N-test was introduced by Schorlemmer et al (2007) and modified by Zechar et al (2010). The observed number of events is given by,\n",
     "\n",
     "$$N_{obs} = \\sum_{m_i, s_j \\in R} \\omega(m_i, s_j).$$\n",
     "\n",
@@ -338,7 +368,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -416,7 +446,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAU40lEQVR4nO3df7xldV3v8ddb4PLTi8IoRhJjCg8vyDQ5449CcyREs6uhYoJwA62USr3oxRDlyuj1FgSllj9KvEH+pChRSAIUUYhAmIFhAC008AcPRZkMaUD5MXzuH+t7YHs4P2fOzPkeej0fj/M4a3/Xd33XZ+199n6ftfbea6WqkCSpN4+Y7wIkSZqIASVJ6pIBJUnqkgElSeqSASVJ6pIBJUnqkgElLUBJNiRZk+T6JGcl2WGKvi9O8pYtXN/KJJXkSSNtb2xty0fa9mvbsSbJD5Lc3KY/P4t1HZxkn7neBs0/A0pamH5UVUur6inAPcDRk3WsqnOq6qQtV9oDrgMOHbl9CPCV0Q5VdV3bjqXAOcCb2+0DZ7GegwED6mHIgJIWvkuBJyXZJcmnk6xNckWSJQBJjkryvjb98rbXdW2SS1rbvkmubHsua5Ps1drf1Ppen+SY1rY4yVeTnJbkhiQXJtl+kro+DfxaW+5ngR8Ct81kg5IclOTyJFe3PcSdWvtJSb7S6jw1yS8CLwZOafU/caPuQXXJgJIWsCRbA7/CsLfyDuCaqloCvBX4yASLvB14flX9HMMLOwx7X+9tezHLgVuSLANeBTwDeCbw20l+vvXfC3h/Ve0L3A68bJLy7gC+neQpwGHAX89wmxYBJwAHVtVTgVXAm5LsArwE2Ldt47uq6p/4yT2vf53JOrQwGFDSwrR9kjUML97fAv4f8CzgowBV9QVg1yQ7j1vuMuCMJL8NbNXaLgfemuQ4YM+q+lEb6+yqurOq1gOfAp7d+t9cVWva9Gpg8RR1nslwmO9g4OwZbtszGQ7ZXda28UhgT4bA+zHw4SQvBe6a4XhaoAwoaWEaew9qaVW9vqruATJBv5842WZVHc2wd7IHsCbJrlX1CYa9qR8BFyQ5YJKxxtw9Mr0B2HqKvucC/wP4VlXdMdaY5CUjH45YPm6ZAJ8b2b59quo3q+o+4OnA3zEE3vlTrFcPAwaU9PBxCXA4QJIVwLrRUGjtT6yqL1fV24F1wB7t/aGbqupPGQ6XLWljHZxkhyQ7Mhxau3S2BbW9seOA/zuu/eyRAFo1brErgP3HPgHYati7vQ+1c1WdBxwDLG39/wN45GxrU/+m+s9H0sKyEjg9yVqGw19HTtDnlPYhiAAXAdcCbwGOSHIvcCvwzqr6QZIzgCvbch+uqmuSLJ5tUVV15iz735bkKOCTSbZtzScwBNFnkmzX6n9jm3cmcFqSNwCH+D7Uw0e83IYkqUce4pMkdcmAkiR1yYCSJHXJgJIkdclP8QmARYsW1eLFi+e7DEn/iaxevXpdVT1msvkGlABYvHgxq1aN/zqKJG0+Sb451XwP8UmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQEmSumRASZK6ZEBJkrpkQGmjrVy5cr5LkNSJzfF6kKqa80G18CxfvrxWrVo1q2WSMN3fz+NOfRzfu/N7D2nfbcfduPXYW2e1Pkn9msnrwQTLrK6q5ZPNn3YPKsniJNfPYoUrkxw70/5TjHNMkh1m2y/JWzd13TNY55OTrElyTZInJnnlHI79jSSL5mCc9XNRz6aaKJymapekMVvPdwFTOAb4GHDXLPu9FfiD2awoyVZVtWEWixwMfKaqTkyyAngl8InNuL5urVixYuoOz92EZSX9pzbT96C2SnJakhuSXJhk+7bncH6S1UkuTfLk8Qsl+WKSdye5JMlXkzwtyaeSfC3Ju1qfHZN8Nsm1Sa5P8ookbwB2By5OcnHrd1CSy5NcneSsJDuN75fkJGD7tnfz8bbcEUmubG1/kWSr1r4+yTuTfBn4hYk2Osnbk1zV6vpQBi9kCMXfarWdBDy7jf/GJFslOaUttzbJa9tYK1qNnwCum2i7R1b9+rad143dr0l2SfLpNuYVSZa09p2SnN76rk3ysnHbsKjdb786wfa9JsmqJKtuu+22Gf4pSNIWUlVT/gCLgfuApe323wBHABcBe7W2ZwBfaNMrgWPb9BeBk9v0/wS+A/wUsC1wC7Ar8DLgtJH17dx+fwNY1KYXAZcAO7bbxwFvH9+v3V4/Mv3fgHOBbdrtDwC/0aYL+PVptn2XkemPAi+aYBtXAH8/0u81wAlteltgFfCE1u9O4Alt3lTb/fo2/bvAh9v0nwEntukDgDVt+mTgPSPjPHrsfgB2A74MPG+6x3nZsmU1W8OfzzR9VjLpj6SHj5m8HkywzKqa4nVppof4bq6qNW16NUNo/SJwVpKxPttOsuw57fd1wA1V9V2AJDcBe7T2U5Oc3F7oL51gjGcC+wCXtfX9F+DyGdT9y8Ay4Kq23PbA99u8DcDfTbP8c5P8PrADsAtwA0PgTeUgYEmSQ9rtnYG9gHuAK6vq5tY+1XZ/qv1eDby0TT+LIdSoqi8k2TXJzsCBwKFjC1bVv7fJbRj+ifi9qvrSNDVLUndmGlB3j0xvYPjP/PaqWjqLZe8fN879wNZVdWOSZcALgT9McmFVvXPcGAE+V1WHzbDe0eX+qqqOn2Dej2uK94GSbMewx7W8qr6dZCWw3QzX+fqqumDceCsY9qAAmGa7x+6nDTz4GD3wn8CIau0TfXTmPoaAez4wbwG12467TfopPkmaysZ+D+oO4OYkLwdo78383MYMlGR34K6q+hhwKvDUNus/gEe26SuA/ZM8qS2zQ5K9J+gHcG+Sbdr0RcAhSR7bltslyZ4zLG0sjNYl2Qk4ZJJ+49d/AfA7YzUk2TvJjuMXmmK7J3MJcHhbdgWwrqruAC4EXjcy7qPbZAGvBp6c5C3TjL1RTjzxxGn73HrsrdSJ9ZAfP2IuPbzM5PVgtjblU3yHAx9McgLD4aQzgWs3Ypz9gFOS3A/cC/xOa/8Q8A9JvltVz01yFPDJJGOHEk8Abhzfr91em+Tqqjq81Xdhkke08X8P+OZ0RVXV7UlOYzgU9w3gqkm6rgXuS3ItcAbwXoZDoFdnOK54G8On/ma63ZNZCZyeZC3DJxaPbO3vAt6f4asAG4B30A4RVtWGJIcC5ya5o6o+MM06ZsUv6koa4xd1tdlszBd1JWlTZFO/qCtJ0nzo+Yu6W0ySsxk+Cj7quPEfdJAkbTkGFFBVL5nvGiRJP8lDfJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuGVCSpC4ZUJKkLhlQkqQuparmuwZ1IMltwDfneNhFwLo5HnNzsda5t1DqhIVT60KpE2ZW655V9ZjJZhpQ2mySrKqq5fNdx0xY69xbKHXCwql1odQJc1Orh/gkSV0yoCRJXTKgtDl9aL4LmAVrnXsLpU5YOLUulDphDmr1PShJUpfcg5IkdcmAkiR1yYDSnEtySpJ/TrI2ydlJHtXat0nyV0muS/LVJMfPc6mT1trmLUlyeZIbWs3b9Vhnm/8zSdYnOXaeShytZbLH/3lJVrf7cnWSA3qss807PsnXk/xLkufPY5lj9by8/R3en2T5SHuPz6kJa23zZvWcMqC0OXwOeEpVLQFuBMaeNC8Htq2q/YBlwGuTLJ6fEh8wYa1JtgY+BhxdVfsCK4B756tIJr9Px7wb+IctXtXEJqt1HfCi9vgfCXx0nuobM9ljvw9wKLAv8ALgA0m2mrcqB9cDLwUuGdfe43Nqwlo35jllQGnOVdWFVXVfu3kF8PixWcCO7Q91e+Ae4I55KPEBU9R6ELC2qq5t/f6tqjbMR41t/ZPVSZKDgZuAG+ahtIeYrNaquqaqvtPabwC2S7LtfNTY6pnsPv014Myquruqbga+Djx9PmocU1Vfrap/mWgW/T2nJqt11s8pA0qb26t58D/7vwXuBL4LfAs4tap+MF+FTWC01r2BSnJBkquT/P481jXeA3Um2RE4DnjHvFY0udH7dNTLgGuq6u4tXM9kRuv8aeDbI/NuaW096v05NWrWz6mtt0BRehhK8nngcRPMeltVfab1eRtwH/DxNu/pwAZgd+DRwKVJPl9VN3VY69bAs4CnAXcBFyVZXVUXdVbnO4B3V9X6JJurtIfYyFrHlt0XOJnhP+oe65zojtzs38eZSa0T6PY5NYFZP6cMKG2UqjpwqvlJjgT+O/DL9eCX7V4JnF9V9wLfT3IZsJzh8FRvtd4CfKmq1rU+5wFPBTZbQG1knc8ADknyR8CjgPuT/Liq3re56tyEWknyeOBs4Deq6l83Z42wSY/9HiPdHg98Z/yyc226WifR5XNqErN+TnmIT3MuyQsYDju9uKruGpn1LeCADHYEngn883zUOGaKWi8AliTZoR3ffw7wlfmoESavs6qeXVWLq2ox8B7gDzZ3OE1nslrbp+Q+CxxfVZfNU3kPmOKxPwc4NMm2SZ4A7AVcOR81zkB3z6kpzPo55ZkkNOeSfB3YFvi31nRFVR2dZCfgdGAfhsMop1fVKfNUJjB5rW3eEQyf7CrgvKqat/ehpqpzpM9KYH1VnbqFy/sJUzz+JzDcn18b6X5QVX1/S9cI0z72b2N4X+o+4JiqmtdPSCZ5CfBnwGOA24E1VfX8Tp9TE9ba5s3qOWVASZK65CE+SVKXDChJUpcMKElSlwwoSVKXDChJUpcMKGkLSlJJ/njk9rHt4+FbsoYvjp1lOsl5GXdm9I0Yb0WSv5+qPcmLk7ylTZ+R5JBZjL++/d49yd+26aOSzPn3vTbXuNo4BpS0Zd0NvDTJoo1ZuH3Bcc5U1Qur6va5HHOS9ZxTVSdt4hjfqaoZB5sWPgNK2rLuAz4EvHH8jCR7Jrkow/WJLkryM639jCR/kuRi4OR2+4NJLk5yU5LnJPnLDNcDOmNkvA8mWZXh2jsTnkw2yTeSLEpydJI17efmti6SHJTh+j1XJzmrfTGUJC/IcC2lf2S4tMKUJtszSfJ/2vY8Ismbk1zVtv8h9SZZnOT6kabdk5yf5GvtVE9j/Q7LcK2h65OcPIP2VyW5McmXgP2n2xZtOQaUtOW9Hzg8yc7j2t8HfKRdn+jjwJ+OzNsbOLCq/le7/WjgAIagO5fhelD7AvslWdr6vK2qlgNLgOckWTJZQVX151W1lOFEnrcAf9L28k5o630qsAp4U4aLzJ0GvAh4NhOfNHRaLVQeC7wKOJDhlEJPB5YCy5L80jRDLAVeAewHvCLJHkl2ZzgR7QFt/tOSHDxF+08xnHB3f+B5DGdkUCcMKGkLq6o7gI8Abxg36xeAT7TpjzKc+XnMWeOunXNuO7npdcD3quq6qrqf4TpLi1ufX09yNXANQ3jN5MX3vcAXqupchvO67QNclmQNw0UG9wSeDNxcVV9rNXxsBuOO97+BR1XVa9sYB7Wfa4Cr2zr2mmaMi6rqh1X1Y4Zzuu3JELBfrKrb2rWePg780hTtzxhpvwf4643YFm0mns1cmh/vYXghPn2KPqPnIbtz3Lyx6yjdPzI9dnvrdpLTY4GnVdW/t0N/U15eO8lRDC/yrxtrAj5XVYeN67eUTb/8xFUMe0m7tOsXBfjDqvqLWYwxut0bGF7PJrvmyFTXIvF8b51yD0qaB+1F+W+A3xxp/ieGS40DHA784yas4r8yhNoPk+wG/MpUnZMsYwi0I9qeGAxXmd0/yZNanx2S7M1wtuwnJHli63fYQwac3vnAScBnkzyS4UzXrx55j+unkzx2I8b9MsPhzEUZLtN+GPCladpXJNk1yTYMl1BXJ9yDkubPH/Pg3goMh/z+MsmbgdsY3pvZKFV1bZJrGA753QRMd3mL1wG7ABdnuPDhqqr6rbZX9ck8eGn2E6rqxiSvYQiXdQxB+pSNqPGsFk7nAC9kOLx5eVv/euAIYFZnOq+q7yY5HriYYa/pvJELE07WvhK4nOGqtFcDW812W7R5eDZzSVKXPMQnSeqSASVJ6pIBJUnqkgElSeqSASVJ6pIBJUnqkgElSerS/weph5TRs1E/+QAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -499,7 +529,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -987,6 +1017,10 @@
    "metadata": {},
    "source": [
     "### References\n",
+    "\n",
+    "Bayona, J.A., Savran, W.H., Rhoades, D.A. and Werner, M.J., 2022. Prospective evaluation of multiplicative hybrid earthquake forecasting models in California. Geophysical Journal International, 229(3), pp.1736-1753.\n",
+    "doi: https://doi.org/10.1093/gji/ggac018\n",
+    "\n",
     "Field, E. H., K. R. Milner, J. L. Hardebeck, M. T. Page, N. J. van der Elst, T. H. Jordan, A. J. Michael, B. E. Shaw, and M. J. Werner (2017). A spatiotemporal clustering model for the third Uniform California Earthquake Rupture Forecast (UCERF3-ETAS): Toward an operational earthquake forecast, Bull. Seismol. Soc. Am. 107, 1049–1081.\n",
     "\n",
     "Harte, D., and D. Vere-Jones (2005), The entropy score and its uses in earthquake forecasting, Pure Appl. Geophys. 162 , 6-7, 1229-1253, DOI: 10.1007/\n",
@@ -1000,6 +1034,16 @@
     "Imoto, M., and D.A. Rhoades (2010), Seismicity models of moderate earthquakes in Kanto, Japan utilizing multiple predictive parameters, Pure Appl. Geophys.\n",
     "167, 6-7, 831-843, DOI: 10.1007/s00024-010-0066-4.\n",
     "\n",
+    "Kato, M., 2019. On the apparently inappropriate use of multiple hypothesis testing in earthquake prediction studies. Seismological Research Letters, 90(3), pp.1330-1334. doi: \n",
+    "https://doi.org/10.1785/0220180378\n",
+    "\n",
+    "\n",
+    "Lombardi, A.M. and Marzocchi, W., 2010. The assumption of Poisson seismic-rate variability in CSEP/RELM experiments. Bulletin of the Seismological Society of America, 100(5A), pp.2293-2300, doi: \n",
+    "https://doi.org/10.1785/0120100012\n",
+    "\n",
+    "Nandan, S., Ouillon, G., Sornette, D. and Wiemer, S., 2019. Forecasting the full distribution of earthquake numbers is fair, robust, and better. Seismological Research Letters, 90(4), pp.1650-1659. doi: \n",
+    "https://doi.org/10.1785/0220180374\n",
+    "\n",
     "Rhoades, D.A, D., Schorlemmer, M.C.Gerstenberger, A. Christophersen, J. D. Zechar & M. Imoto (2011) Efficient testing of earthquake forecasting models, Acta Geophysica 59\n",
     "\n",
     "Savran, W., M. J. Werner, W. Marzocchi, D. Rhoades, D. D. Jackson, K. R. Milner, E. H. Field, and A. J. Michael (2020). Pseudoprospective evaluation of UCERF3-ETAS forecasts during the 2019 Ridgecrest Sequence, Bulletin of the Seismological Society of America.\n",
@@ -1014,8 +1058,12 @@
     "\n",
     "M. Taroni, W. Marzocchi, D. Schorlemmer, M. J. Werner, S. Wiemer, J. D. Zechar, L. Heiniger, F. Euchner; Prospective CSEP Evaluation of 1‐Day, 3‐Month, and 5‐Yr Earthquake Forecasts for Italy. Seismological Research Letters 2018;; 89 (4): 1251–1261. doi: https://doi.org/10.1785/0220180031\n",
     "\n",
+    "\n",
     "Werner, M. J., A. Helmstetter, D. D. Jackson, and Y. Y. Kagan (2011a). High-Resolution Long-Term and Short-Term Earthquake Forecasts for California, Bulletin of the Seismological Society of America 101 1630-1648\n",
     "\n",
+    "Werner, M.J. and Sornette, D., 2008. Magnitude uncertainties impact seismic rate estimates, forecasts, and predictability experiments. Journal of Geophysical Research: Solid Earth, 113(B8). doi: https://doi.org/10.1029/2007JB005427\n",
+    "\n",
+    "\n",
     "Werner, M.J. J.D. Zechar, W. Marzocchi, and S. Wiemer (2011b), Retrospective evaluation of the five-year and ten-year CSEP-Italy earthquake forecasts, Annals of Geophysics 53, no. 3, 11–30, doi:10.4401/ag-4840.\n",
     "\n",
     "Zechar, 2011: Evaluating earthquake predictions and earthquake forecasts: a guide for students and new researchers, CORSSA (http://www.corssa.org/en/articles/theme_6/)\n",
@@ -1025,6 +1073,14 @@
     "Zechar, J.D., D. Schorlemmer, M. Liukis, J. Yu, F. Euchner, P.J. Maechling, and T.H. Jordan (2010b), The Collaboratory for the Study of Earthquake Predictability perspective on computational earthquake science, Concurr. Comp-Pract. E., doi:10.1002/cpe.1519.\n",
     "\n"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fifty-wright",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -1043,7 +1099,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.8"
+   "version": "3.8.6"
   }
  },
  "nbformat": 4,

From 920b3666dfbefce7df5ee193be3b9d82c63540a0 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Thu, 22 Sep 2022 14:53:02 -0700
Subject: [PATCH 20/29] pinned matplotlib version until we implement a
 workaround for the errorbar changes

---
 requirements.txt | 2 +-
 requirements.yml | 2 +-
 setup.py         | 7 ++++---
 3 files changed, 6 insertions(+), 5 deletions(-)

diff --git a/requirements.txt b/requirements.txt
index 6a95af5b..1c56f845 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,7 +1,7 @@
 numpy
 scipy
 pandas
-matplotlib
+matplotlib<=3.5.3
 cartopy
 obspy
 pyproj
diff --git a/requirements.yml b/requirements.yml
index 14caee7e..1dd4d9ab 100644
--- a/requirements.yml
+++ b/requirements.yml
@@ -7,7 +7,7 @@ dependencies:
   - numpy
   - pandas
   - scipy
-  - matplotlib
+  - matplotlib<=3.5.3
   - pyproj
   - obspy
   - python-dateutil
diff --git a/setup.py b/setup.py
index 2a4a26ad..9edc6fd3 100644
--- a/setup.py
+++ b/setup.py
@@ -12,6 +12,7 @@ def get_version():
         raise RuntimeError("Unable to find version string in %s." % (VERSIONFILE,))
     return verstr
 
+
 with open("README.md",'r') as fh:
     long_description = fh.read()
 
@@ -25,11 +26,11 @@ def get_version():
     description='Python tools from the Collaboratory for the Study of Earthquake Predictability',
     long_description=long_description,
     long_description_content_type='text/markdown',
-    install_requires = [
-        'numpy<=1.21.5',
+    install_requires=[
+        'numpy',
         'scipy',
         'pandas',
-        'matplotlib',
+        'matplotlib<=3.5.3',
         'cartopy',
         'obspy',
         'pyproj',

From 55f3abd9b800d05fb710a71b9fe810643b000e68 Mon Sep 17 00:00:00 2001
From: Pablo Iturrieta <69042881+pabloitu@users.noreply.github.com>
Date: Mon, 14 Nov 2022 19:59:01 +0100
Subject: [PATCH 21/29] feat: Added query_bsi (#201)

* feat: Added query_bsi, based on comcat query functions. Can be called from csep.__init__, wrapping the readers._query_bsi. This is based in csep.utils.comcat.search functions.
mods: (i) Exception catchs for Hostname mismatch in SSL verification (the bsi does not go through https). (ii) in comcat and bsi, ids are set different. SummaryEvent now handles this with try/except. (iii) bsi returns datetimes as utc strings, instead of timestamp as comcat.
* docs: added query_bsi to api reference and mentioned it in tutorial/catalog_filtering
styl: modified query_comcat docstring
* fix: added maxdepth to query_comcat and query_bsi wrappers at top and bottom level. default=1000. Maybe these functions should have the arguments to completely define an experiment catalog (perhaps just max_mag and its ready)
---
 csep/__init__.py                        | 64 +++++++++++++++++++++++--
 csep/utils/comcat.py                    | 48 +++++++++++++++++--
 csep/utils/readers.py                   | 28 +++++++++--
 docs/reference/api_reference.rst        |  1 +
 examples/tutorials/catalog_filtering.py |  5 +-
 tests/artifacts/BSI/vcr_search.yaml     | 46 ++++++++++++++++++
 tests/artifacts/BSI/vcr_summary.yaml    | 46 ++++++++++++++++++
 tests/test_bsi.py                       | 42 ++++++++++++++++
 8 files changed, 268 insertions(+), 12 deletions(-)
 create mode 100644 tests/artifacts/BSI/vcr_search.yaml
 create mode 100644 tests/artifacts/BSI/vcr_summary.yaml
 create mode 100644 tests/test_bsi.py

diff --git a/csep/__init__.py b/csep/__init__.py
index 4149d43c..de1a03f8 100644
--- a/csep/__init__.py
+++ b/csep/__init__.py
@@ -188,7 +188,9 @@ def load_catalog(filename, type='csep-csv', format='native', loader=None, apply_
 
 def query_comcat(start_time, end_time, min_magnitude=2.50,
                  min_latitude=31.50, max_latitude=43.00,
-                 min_longitude=-125.40, max_longitude=-113.10, verbose=True,
+                 min_longitude=-125.40, max_longitude=-113.10,
+                 max_depth=1000,
+                 verbose=True,
                  apply_filters=False, **kwargs):
     """
     Access Comcat catalog through web service
@@ -201,11 +203,11 @@ def query_comcat(start_time, end_time, min_magnitude=2.50,
         max_latitude: max latitude of bounding box
         min_longitude: min latitude of bounding box
         max_longitude: max longitude of bounding box
-        region: :class:`csep.core.regions.CartesianGrid2D
+        max_depth: maximum depth of the bounding box
         verbose (bool): print catalog summary statistics
 
     Returns:
-        :class:`csep.core.catalogs.ComcatCatalog
+        :class:`csep.core.catalogs.CSEPCatalog
     """
 
     # Timezone should be in UTC
@@ -213,7 +215,8 @@ def query_comcat(start_time, end_time, min_magnitude=2.50,
     eventlist = readers._query_comcat(start_time=start_time, end_time=end_time,
                            min_magnitude=min_magnitude,
                            min_latitude=min_latitude, max_latitude=max_latitude,
-                           min_longitude=min_longitude, max_longitude=max_longitude)
+                           min_longitude=min_longitude, max_longitude=max_longitude,
+                           max_depth=max_depth)
     t1 = time.time()
     comcat = catalogs.CSEPCatalog(data=eventlist, date_accessed=utc_now_datetime(), **kwargs)
     print("Fetched ComCat catalog in {} seconds.\n".format(t1 - t0))
@@ -234,6 +237,59 @@ def query_comcat(start_time, end_time, min_magnitude=2.50,
 
     return comcat
 
+
+def query_bsi(start_time, end_time, min_magnitude=2.50,
+              min_latitude=32.0, max_latitude=50.0,
+              min_longitude=2.0, max_longitude=21.0,
+              max_depth=1000,
+              verbose=True,
+              apply_filters=False, **kwargs):
+    """
+    Access BSI catalog through web service
+
+    Args:
+        start_time: datetime object of start of catalog
+        end_time: datetime object for end of catalog
+        min_magnitude: minimum magnitude to query
+        min_latitude:  maximum magnitude to query
+        max_latitude: max latitude of bounding box
+        min_longitude: min latitude of bounding box
+        max_longitude: max longitude of bounding box
+        max_depth: maximum depth of the bounding box
+        verbose (bool): print catalog summary statistics
+
+    Returns:
+        :class:`csep.core.catalogs.CSEPCatalog
+    """
+
+    # Timezone should be in UTC
+    t0 = time.time()
+    eventlist = readers._query_bsi(start_time=start_time, end_time=end_time,
+                                   min_magnitude=min_magnitude,
+                                   min_latitude=min_latitude, max_latitude=max_latitude,
+                                   min_longitude=min_longitude, max_longitude=max_longitude,
+                                   max_depth=max_depth)
+    t1 = time.time()
+    bsi = catalogs.CSEPCatalog(data=eventlist, date_accessed=utc_now_datetime(), **kwargs)
+    print("Fetched BSI catalog in {} seconds.\n".format(t1 - t0))
+
+    if apply_filters:
+        try:
+            bsi = bsi.filter().filter_spatial()
+        except CSEPCatalogException:
+            bsi = bsi.filter()
+
+    if verbose:
+        print("Downloaded catalog from Bollettino Sismico Italiano (BSI) with following parameters")
+        print("Start Date: {}\nEnd Date: {}".format(str(bsi.start_time), str(bsi.end_time)))
+        print("Min Latitude: {} and Max Latitude: {}".format(bsi.min_latitude, bsi.max_latitude))
+        print("Min Longitude: {} and Max Longitude: {}".format(bsi.min_longitude, bsi.max_longitude))
+        print("Min Magnitude: {}".format(bsi.min_magnitude))
+        print(f"Found {bsi.event_count} events in the BSI catalog.")
+
+    return bsi
+
+
 def load_evaluation_result(fname):
     """ Load evaluation result stored as json file
 
diff --git a/csep/utils/comcat.py b/csep/utils/comcat.py
index da0d2558..ecaea5f9 100644
--- a/csep/utils/comcat.py
+++ b/csep/utils/comcat.py
@@ -1,8 +1,9 @@
 # python imports
-from datetime import datetime, timedelta
+from datetime import datetime, timedelta, timezone
 from urllib import request
-from urllib.error import HTTPError
+from urllib.error import HTTPError, URLError
 from urllib.parse import urlparse, urlencode
+import ssl
 import json
 import time
 from collections import OrderedDict
@@ -293,6 +294,39 @@ def _search(**newargs):
             except Exception as msg:
                 raise Exception(
                     'Error downloading data from url %s.  "%s".' % (url, msg))
+
+    except ssl.SSLCertVerificationError as SSLe:
+        # Fails to verify SSL certificate, when there is a hostname mismatch
+        if SSLe.verify_code == 62:
+            try:
+                context = ssl._create_unverified_context()
+                fh = request.urlopen(url, timeout=TIMEOUT, context=context)
+                data = fh.read().decode('utf8')
+                fh.close()
+                jdict = json.loads(data)
+                events = []
+                for feature in jdict['features']:
+                    events.append(SummaryEvent(feature))
+            except Exception as msg:
+                raise Exception(
+                    'Error downloading data from url %s.  "%s".' % (url, msg))
+
+    except URLError as URLe:
+        # Fails to verify SSL certificate, when there is a hostname mismatch
+        if isinstance(URLe.reason, ssl.SSLCertVerificationError) and URLe.reason.verify_code == 62:
+            try:
+                context = ssl._create_unverified_context()
+                fh = request.urlopen(url, timeout=TIMEOUT, context=context)
+                data = fh.read().decode('utf8')
+                fh.close()
+                jdict = json.loads(data)
+                events = []
+                for feature in jdict['features']:
+                    events.append(SummaryEvent(feature))
+            except Exception as msg:
+                raise Exception(
+                    'Error downloading data from url %s.  "%s".' % (url, msg))
+
     except Exception as msg:
         raise Exception(
             'Error downloading data from url %s.  "%s".' % (url, msg))
@@ -358,7 +392,11 @@ def id(self):
         Returns:
             str: Authoritative origin ID.
         """
-        return self._jdict['id']
+        ## comcat has an id key in each feature, whereas bsi has eventId within the properties dict
+        try:
+            return self._jdict['id']
+        except:
+            return self._jdict['properties']['eventId']
 
     @property
     def time(self):
@@ -367,6 +405,10 @@ def time(self):
             datetime: Authoritative origin time.
         """
         time_in_msec = self._jdict['properties']['time']
+        # Comcat gives the event time in a ms timestamp, whereas bsi in datetime isoformat
+        if isinstance(time_in_msec, str):
+            event_dtime = datetime.fromisoformat(time_in_msec).replace(tzinfo=timezone.utc)
+            time_in_msec = event_dtime.timestamp() * 1000
         time_in_sec = time_in_msec // 1000
         msec = time_in_msec - (time_in_sec * 1000)
         dtime = datetime.utcfromtimestamp(time_in_sec)
diff --git a/csep/utils/readers.py b/csep/utils/readers.py
index b5352279..4569634b 100644
--- a/csep/utils/readers.py
+++ b/csep/utils/readers.py
@@ -655,8 +655,9 @@ def jma_csv(fname):
     return events
 
 def _query_comcat(start_time, end_time, min_magnitude=2.50,
-                 min_latitude=31.50, max_latitude=43.00,
-                 min_longitude=-125.40, max_longitude=-113.10, extra_comcat_params=None):
+                  min_latitude=31.50, max_latitude=43.00,
+                  min_longitude=-125.40, max_longitude=-113.10,
+                  max_depth=1000, extra_comcat_params=None):
     """
     Return eventlist from ComCat web service.
 
@@ -668,6 +669,7 @@ def _query_comcat(start_time, end_time, min_magnitude=2.50,
         max_latitude (float): maximum latitude of query
         min_longitude (float): minimum longitude of query
         max_longitude (float): maximum longitude of query
+        max_depth (float): maximum depth of query
         extra_comcat_params (dict): additional parameters to pass to comcat search function
 
     Returns:
@@ -679,10 +681,30 @@ def _query_comcat(start_time, end_time, min_magnitude=2.50,
     eventlist = search(minmagnitude=min_magnitude,
         minlatitude=min_latitude, maxlatitude=max_latitude,
         minlongitude=min_longitude, maxlongitude=max_longitude,
-        starttime=start_time, endtime=end_time, **extra_comcat_params)
+        starttime=start_time, endtime=end_time,
+        maxdepth=max_depth, **extra_comcat_params)
 
     return eventlist
 
+def _query_bsi(start_time, end_time, min_magnitude=2.50,
+               min_latitude=32.0, max_latitude=50.0,
+               min_longitude=2.0, max_longitude=21.0,
+               max_depth=1000, extra_bsi_params=None):
+    """
+    Queries INGV Bulletino Sismico Italiano, revised version.
+    :return: csep.core.Catalog object
+    """
+    extra_bsi_params = extra_bsi_params or {}
+    bsi_host = 'webservices.rm.ingv.it'
+    extra_bsi_params.update({'host': bsi_host, 'limit': 15000, 'offset': 0})
+    # get eventlist from Comcat
+    eventlist = search(minmagnitude=min_magnitude,
+                       minlatitude=min_latitude, maxlatitude=max_latitude,
+                       minlongitude=min_longitude, maxlongitude=max_longitude,
+                       maxdepth=max_depth,
+                       starttime=start_time, endtime=end_time, **extra_bsi_params)
+
+    return eventlist
 def _parse_datetime_to_zmap(date, time):
         """ Helping function to return datetime in zmap format.
 
diff --git a/docs/reference/api_reference.rst b/docs/reference/api_reference.rst
index 9f8a6b36..6e3ce176 100644
--- a/docs/reference/api_reference.rst
+++ b/docs/reference/api_reference.rst
@@ -16,6 +16,7 @@ Loading catalogs and forecasts
    load_stochastic_event_sets
    load_catalog
    query_comcat
+   query_bsi
    load_gridded_forecast
    load_catalog_forecast
 
diff --git a/examples/tutorials/catalog_filtering.py b/examples/tutorials/catalog_filtering.py
index 406ee565..a21937ff 100644
--- a/examples/tutorials/catalog_filtering.py
+++ b/examples/tutorials/catalog_filtering.py
@@ -30,8 +30,9 @@
 # Load catalog
 # ------------
 #
-# PyCSEP provides access to the ComCat web API using :func:`csep.query_comcat`. This function requires a
-# :class:`datetime.datetime` to specify the start and end dates.
+# PyCSEP provides access to the ComCat web API using :func:`csep.query_comcat` and to the Bollettino Sismico Italiano
+# API using :func:`csep.query_bsi`. These functions require a :class:`datetime.datetime` to specify the start and end
+# dates.
 
 start_time = csep.utils.time_utils.strptime_to_utc_datetime('2019-01-01 00:00:00.0')
 end_time = csep.utils.time_utils.utc_now_datetime()
diff --git a/tests/artifacts/BSI/vcr_search.yaml b/tests/artifacts/BSI/vcr_search.yaml
new file mode 100644
index 00000000..76053c90
--- /dev/null
+++ b/tests/artifacts/BSI/vcr_search.yaml
@@ -0,0 +1,46 @@
+interactions:
+- request:
+    body: null
+    headers:
+      Connection:
+      - close
+      Host:
+      - webservices.rm.ingv.it
+      User-Agent:
+      - Python-urllib/3.10
+    method: GET
+    uri: https://webservices.rm.ingv.it/fdsnws/event/1/query?format=geojson&starttime=2009-04-06T00%3A00%3A00&endtime=2009-04-07T00%3A00%3A00&limit=15000&maxdepth=1000&maxmagnitude=10.0&mindepth=-100&minmagnitude=5.5&offset=0&orderby=time-asc&eventtype=earthquake
+  response:
+    body:
+      string: '{"type":"FeatureCollection","features":[{"type":"Feature","properties":{"eventId":1895389,"originId":755599,"time":"2009-04-06T01:32:40.400000","author":"BULLETIN-SISPICK","magType":"Mw","mag":6.1,"magAuthor":"--","type":"earthquake","place":"2
+        km SW L''Aquila (AQ)","version":1000,"geojson_creationTime":"2022-09-21T12:18:03"},"geometry":{"type":"Point","coordinates":[13.38,42.342,8.3]}}]}'
+    headers:
+      Access-Control-Allow-Origin:
+      - '*'
+      Cache-Control:
+      - public, max-age=60
+      Connection:
+      - close
+      Content-Type:
+      - application/json
+      Date:
+      - Wed, 21 Sep 2022 12:18:03 GMT
+      Server:
+      - nginx
+      Transfer-Encoding:
+      - chunked
+      Vary:
+      - Accept-Encoding
+      - Accept-Encoding
+      X-Cache-Status:
+      - EXPIRED
+      X-RateLimit-Limit:
+      - '10'
+      X-RateLimit-Reset:
+      - '1'
+      X-UA-Compatible:
+      - IE=Edge
+    status:
+      code: 200
+      message: OK
+version: 1
diff --git a/tests/artifacts/BSI/vcr_summary.yaml b/tests/artifacts/BSI/vcr_summary.yaml
new file mode 100644
index 00000000..9349aa3d
--- /dev/null
+++ b/tests/artifacts/BSI/vcr_summary.yaml
@@ -0,0 +1,46 @@
+interactions:
+- request:
+    body: null
+    headers:
+      Connection:
+      - close
+      Host:
+      - webservices.rm.ingv.it
+      User-Agent:
+      - Python-urllib/3.10
+    method: GET
+    uri: https://webservices.rm.ingv.it/fdsnws/event/1/query?format=geojson&starttime=2009-04-06T00%3A00%3A00&endtime=2009-04-07T00%3A00%3A00&limit=15000&maxdepth=1000&maxmagnitude=10.0&mindepth=-100&minmagnitude=5.5&offset=0&orderby=time-asc&eventtype=earthquake
+  response:
+    body:
+      string: '{"type":"FeatureCollection","features":[{"type":"Feature","properties":{"eventId":1895389,"originId":755599,"time":"2009-04-06T01:32:40.400000","author":"BULLETIN-SISPICK","magType":"Mw","mag":6.1,"magAuthor":"--","type":"earthquake","place":"2
+        km SW L''Aquila (AQ)","version":1000,"geojson_creationTime":"2022-09-21T12:14:55"},"geometry":{"type":"Point","coordinates":[13.38,42.342,8.3]}}]}'
+    headers:
+      Access-Control-Allow-Origin:
+      - '*'
+      Cache-Control:
+      - public, max-age=60
+      Connection:
+      - close
+      Content-Type:
+      - application/json
+      Date:
+      - Wed, 21 Sep 2022 12:14:55 GMT
+      Server:
+      - nginx
+      Transfer-Encoding:
+      - chunked
+      Vary:
+      - Accept-Encoding
+      - Accept-Encoding
+      X-Cache-Status:
+      - MISS
+      X-RateLimit-Limit:
+      - '10'
+      X-RateLimit-Reset:
+      - '1'
+      X-UA-Compatible:
+      - IE=Edge
+    status:
+      code: 200
+      message: OK
+version: 1
diff --git a/tests/test_bsi.py b/tests/test_bsi.py
new file mode 100644
index 00000000..4673bfc8
--- /dev/null
+++ b/tests/test_bsi.py
@@ -0,0 +1,42 @@
+from datetime import datetime
+import os.path
+import vcr
+from csep.utils.comcat import search
+
+HOST = 'webservices.rm.ingv.it'
+
+
+def get_datadir():
+    root_dir = os.path.dirname(os.path.abspath(__file__))
+    data_dir = os.path.join(root_dir, 'artifacts', 'BSI')
+    return data_dir
+
+
+def test_search():
+    datadir = get_datadir()
+    tape_file = os.path.join(datadir, 'vcr_search.yaml')
+    with vcr.use_cassette(tape_file):
+        # L'Aquila
+        eventlist = search(starttime=datetime(2009, 4, 6, 0, 0, 0),
+                           endtime=datetime(2009, 4, 7, 0, 0, 0),
+                           minmagnitude=5.5, host=HOST, limit=15000, offset=0)
+        event = eventlist[0]
+        assert event.id == 1895389
+
+
+def test_summary():
+    datadir = get_datadir()
+    tape_file = os.path.join(datadir, 'vcr_summary.yaml')
+    with vcr.use_cassette(tape_file):
+        eventlist = search(starttime=datetime(2009, 4, 6, 0, 0, 0),
+                           endtime=datetime(2009, 4, 7, 0, 0, 0),
+                           minmagnitude=5.5, host=HOST, limit=15000, offset=0)
+        event = eventlist[0]
+        cmp = '1895389 2009-04-06 01:32:40.400000 (42.342,13.380) 8.3 km M6.1'
+        assert str(event) == cmp
+        assert event.id == 1895389
+        assert event.time == datetime(2009, 4, 6, 1, 32, 40, 400000)
+        assert event.latitude == 42.342
+        assert event.longitude == 13.380
+        assert event.depth == 8.3
+        assert event.magnitude == 6.1

From ec78dd0046956d40b0df87128c776cd21ebcd3d2 Mon Sep 17 00:00:00 2001
From: khawajasim <asimkhawaja786@gmail.com>
Date: Mon, 14 Nov 2022 20:01:53 +0100
Subject: [PATCH 22/29] Binomial testing (#208)

* added to unit test for binary_joint_LL
---
 csep/core/binomial_evaluations.py |  4 ++--
 tests/test_evaluations.py         | 16 ++++++++++++++++
 2 files changed, 18 insertions(+), 2 deletions(-)

diff --git a/csep/core/binomial_evaluations.py b/csep/core/binomial_evaluations.py
index 9ecd61ea..ec187cf4 100644
--- a/csep/core/binomial_evaluations.py
+++ b/csep/core/binomial_evaluations.py
@@ -88,13 +88,13 @@ def binary_joint_log_likelihood_ndarray(forecast, catalog):
                     It has to be a either zero or positive integer only (No Floating Point)
     """
     #First, we mask the forecast in cells where we could find log=0.0 singularities:
-    forecast_masked = np.ma.masked_where(forecast.ravel() <= 0.0, forecast.ravel()) 
+    forecast_masked = numpy.ma.masked_where(forecast.ravel() <= 0.0, forecast.ravel())
     
     #Then, we compute the log-likelihood of observing one or more events given a Poisson distribution, i.e., 1 - Pr(0) 
     target_idx = numpy.nonzero(catalog.ravel())
     y = numpy.zeros(forecast_masked.ravel().shape)
     y[target_idx[0]] = 1
-    first_term = y * (np.log(1.0 - np.exp(-forecast_masked.ravel())))
+    first_term = y * (numpy.log(1.0 - numpy.exp(-forecast_masked.ravel())))
     
     #Also, we estimate the log-likelihood in cells no events are observed:
     second_term = (1-y) * (-forecast_masked.ravel().data)
diff --git a/tests/test_evaluations.py b/tests/test_evaluations.py
index df6e22e6..ffc6f3ce 100644
--- a/tests/test_evaluations.py
+++ b/tests/test_evaluations.py
@@ -3,6 +3,8 @@
 import unittest
 
 from csep.core.poisson_evaluations import _simulate_catalog, _poisson_likelihood_test
+from csep.core.binomial_evaluations import binary_joint_log_likelihood_ndarray
+
 
 def get_datadir():
     root_dir = os.path.dirname(os.path.abspath(__file__))
@@ -71,3 +73,17 @@ def test_likelihood(self):
         # calculated by hand given the expected data, see explanation in zechar et al., 2010.
         numpy.testing.assert_allclose(simulated_ll[0], -7.178053830347945)
 
+
+class TestBinomialLikelihood(unittest.TestCase):
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+        self.forecast_data = numpy.array([[0.1, 0.3, 0.4], [0.2, 0.1, 0.1]])
+        self.observed_data = numpy.array([[0, 1, 2], [1, 1, 0]])
+
+    def test_likelihood(self):
+        bill = binary_joint_log_likelihood_ndarray(self.forecast_data, self.observed_data)
+
+        numpy.testing.assert_allclose(bill, -6.7197988064)
+
+if __name__ == '__main__':
+    unittest.main()
\ No newline at end of file

From 94dee18c48ae81bd1a128f77289518c693f9f045 Mon Sep 17 00:00:00 2001
From: bayonato89 <72937672+bayonato89@users.noreply.github.com>
Date: Mon, 14 Nov 2022 19:55:56 +0000
Subject: [PATCH 23/29] Non poissonian tests (#205)

* Added non-Poissonian comparative and consistency tests.
* Added a _simulate_catalog function for binary likelihood tests

Co-authored-by: wsavran <35315438+wsavran@users.noreply.github.com>
---
 csep/core/binomial_evaluations.py | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/csep/core/binomial_evaluations.py b/csep/core/binomial_evaluations.py
index ec187cf4..0c9346b6 100644
--- a/csep/core/binomial_evaluations.py
+++ b/csep/core/binomial_evaluations.py
@@ -102,6 +102,29 @@ def binary_joint_log_likelihood_ndarray(forecast, catalog):
     return sum(first_term.data + second_term.data)
     
     
+def _simulate_catalog(num_events, sampling_weights, sim_fore, random_numbers=None):
+
+    # generate uniformly distributed random numbers in [0,1), this
+    if random_numbers is None:
+        random_numbers = numpy.random.rand(num_events)
+    else:
+        # TODO: ensure that random numbers are all between 0 and 1.
+        pass
+
+    # reset simulation array to zero, but don't reallocate
+    sim_fore.fill(0)
+
+    eqs = 0
+    while eqs < num_events:
+            random_num = numpy.random.uniform(0,1)
+            loc = numpy.searchsorted(sampling_weights, random_num)
+            if sim_fore[loc] == 0:
+                numpy.add.at(sim_fore, loc, 1)
+                eqs = eqs+1
+    
+    return sim_fore    
+    
+
 def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000, random_numbers=None, 
                               seed=None, use_observed_counts=True, verbose=True, normalize_likelihood=False):
     """  Computes binary conditional-likelihood test from CSEP using an efficient simulation based approach.

From ebbe3ba3258add3b1ab4f8cd2dd76694069eb044 Mon Sep 17 00:00:00 2001
From: Pablo Iturrieta <69042881+pabloitu@users.noreply.github.com>
Date: Tue, 15 Nov 2022 17:11:15 +0100
Subject: [PATCH 24/29] Fix consistency plots (#206)

* style: formatted function plot_consistency_test to use original dependencies aliases
* fix: changed errorbar to be defined from the test distribution mean.
* feat: added option to plot test distribution's mean.
* styl: homogenized plot_poisson_consistency_test and plot_consistency_test
* build: removed matplotlib pin
---
 csep/utils/plots.py | 54 +++++++++++++++++++++++++++++++--------------
 requirements.txt    |  2 +-
 requirements.yml    |  2 +-
 setup.py            |  2 +-
 4 files changed, 40 insertions(+), 20 deletions(-)

diff --git a/csep/utils/plots.py b/csep/utils/plots.py
index 3c594805..f4369fb0 100644
--- a/csep/utils/plots.py
+++ b/csep/utils/plots.py
@@ -1557,7 +1557,7 @@ def plot_poisson_consistency_test(eval_results, normalize=False, one_sided_lower
     figsize= plot_args.get('figsize', None)
     title = plot_args.get('title', results[0].name)
     title_fontsize = plot_args.get('title_fontsize', None)
-    xlabel = plot_args.get('xlabel', 'X')
+    xlabel = plot_args.get('xlabel', '')
     xlabel_fontsize = plot_args.get('xlabel_fontsize', None)
     xticks_fontsize = plot_args.get('xticks_fontsize', None)
     ylabel_fontsize = plot_args.get('ylabel_fontsize', None)
@@ -1567,6 +1567,7 @@ def plot_poisson_consistency_test(eval_results, normalize=False, one_sided_lower
     hbars = plot_args.get('hbars', True)
     tight_layout = plot_args.get('tight_layout', True)
     percentile = plot_args.get('percentile', 95)
+    plot_mean = plot_args.get('mean', False)
 
     if axes is None:
         fig, ax = pyplot.subplots(figsize=figsize)
@@ -1580,6 +1581,7 @@ def plot_poisson_consistency_test(eval_results, normalize=False, one_sided_lower
         if res.test_distribution[0] == 'poisson':
             plow = scipy.stats.poisson.ppf((1 - percentile/100.)/2., res.test_distribution[1])
             phigh = scipy.stats.poisson.ppf(1 - (1 - percentile/100.)/2., res.test_distribution[1])
+            mean = res.test_distribution[1]
             observed_statistic = res.observed_statistic
         # empirical distributions
         else:
@@ -1596,12 +1598,14 @@ def plot_poisson_consistency_test(eval_results, normalize=False, one_sided_lower
             else:
                 plow = numpy.percentile(test_distribution, (100 - percentile)/2.)
                 phigh = numpy.percentile(test_distribution, 100 - (100 - percentile)/2.)
+            mean = numpy.mean(res.test_distribution)
 
         if not numpy.isinf(observed_statistic): # Check if test result does not diverges
-            low = observed_statistic - plow
-            high = phigh - observed_statistic
-            ax.errorbar(observed_statistic, index, xerr=numpy.array([[low, high]]).T,
-                        fmt=_get_marker_style(observed_statistic, (plow, phigh), one_sided_lower),
+            percentile_lims = numpy.array([[mean - plow,  phigh - mean]]).T
+            ax.plot(observed_statistic, index,
+                    _get_marker_style(observed_statistic, (plow, phigh), one_sided_lower))
+            ax.errorbar(mean, index, xerr=percentile_lims,
+                        fmt='ko'*plot_mean,
                         capsize=capsize, linewidth=linewidth, ecolor=color)
             # determine the limits to use
             xlims.append((plow, phigh, observed_statistic))
@@ -1887,7 +1891,7 @@ def add_labels_for_publication(figure, style='bssa', labelsize=16):
     return
 
 
-def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, plot_args=None, variance=None):
+def plot_consistency_test(eval_results, normalize=False, axes=None, one_sided_lower=False, variance=None, plot_args=None, show=False):
     """ Plots results from CSEP1 tests following the CSEP1 convention.
 
     Note: All of the evaluations should be from the same type of evaluation, otherwise the results will not be
@@ -1927,8 +1931,10 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
     # Parse plot arguments. More can be added here
     if plot_args is None:
         plot_args = {}
-    figsize= plot_args.get('figsize', (7,8))
-    xlabel = plot_args.get('xlabel', 'X')
+    figsize= plot_args.get('figsize', None)
+    title = plot_args.get('title', results[0].name)
+    title_fontsize = plot_args.get('title_fontsize', None)
+    xlabel = plot_args.get('xlabel', '')
     xlabel_fontsize = plot_args.get('xlabel_fontsize', None)
     xticks_fontsize = plot_args.get('xticks_fontsize', None)
     ylabel_fontsize = plot_args.get('ylabel_fontsize', None)
@@ -1938,8 +1944,14 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
     hbars = plot_args.get('hbars', True)
     tight_layout = plot_args.get('tight_layout', True)
     percentile = plot_args.get('percentile', 95)
+    plot_mean = plot_args.get('mean', False)
+
+    if axes is None:
+        fig, ax = pyplot.subplots(figsize=figsize)
+    else:
+        ax = axes
+        fig = ax.get_figure()
 
-    fig, ax = pyplot.subplots(figsize=figsize)
     xlims = []
     
     for index, res in enumerate(results):
@@ -1947,6 +1959,7 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
         if res.test_distribution[0] == 'poisson':
             plow = scipy.stats.poisson.ppf((1 - percentile/100.)/2., res.test_distribution[1])
             phigh = scipy.stats.poisson.ppf(1 - (1 - percentile/100.)/2., res.test_distribution[1])
+            mean = res.test_distribution[1]
             observed_statistic = res.observed_statistic
         
         elif res.test_distribution[0] == 'negative_binomial':
@@ -1973,13 +1986,15 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
             else:
                 plow = numpy.percentile(test_distribution, 2.5)
                 phigh = numpy.percentile(test_distribution, 97.5)
+            mean = numpy.mean(res.test_distribution)
 
         if not numpy.isinf(observed_statistic): # Check if test result does not diverges
-            low = observed_statistic - plow
-            high = phigh - observed_statistic
-            ax.errorbar(observed_statistic, index, xerr=numpy.array([[low, high]]).T,
-                        fmt=_get_marker_style(observed_statistic, (plow, phigh), one_sided_lower),
-                        capsize=4, linewidth=linewidth, ecolor=color, markersize = 10, zorder=1)
+            percentile_lims = numpy.array([[mean - plow,  phigh - mean]]).T
+            ax.plot(observed_statistic, index,
+                    _get_marker_style(observed_statistic, (plow, phigh), one_sided_lower))
+            ax.errorbar(mean, index, xerr=percentile_lims,
+                        fmt='ko'*plot_mean,
+                        capsize=capsize, linewidth=linewidth, ecolor=color)
             # determine the limits to use
             xlims.append((plow, phigh, observed_statistic))
             # we want to only extent the distribution where it falls outside of it in the acceptable tail
@@ -2001,18 +2016,23 @@ def plot_consistency_test(eval_results, normalize=False, one_sided_lower=True, p
     except ValueError:
         raise ValueError('All EvaluationResults have infinite observed_statistics')
     ax.set_yticks(numpy.arange(len(results)))
-    ax.set_yticklabels([res.sim_name for res in results], fontsize=14)
+    ax.set_yticklabels([res.sim_name for res in results], fontsize=ylabel_fontsize)
     ax.set_ylim([-0.5, len(results)-0.5])
     if hbars:
         yTickPos = ax.get_yticks()
         if len(yTickPos) >= 2:
             ax.barh(yTickPos, numpy.array([99999] * len(yTickPos)), left=-10000,
                     height=(yTickPos[1] - yTickPos[0]), color=['w', 'gray'], alpha=0.2, zorder=0)
-    ax.set_xlabel(xlabel, fontsize=14)
-    ax.tick_params(axis='x', labelsize=13)
+    ax.set_title(title, fontsize=title_fontsize)
+    ax.set_xlabel(xlabel, fontsize=xlabel_fontsize)
+    ax.tick_params(axis='x', labelsize=xticks_fontsize)
     if tight_layout:
         ax.figure.tight_layout()
         fig.tight_layout()
+
+    if show:
+        pyplot.show()
+
     return ax
     
 
diff --git a/requirements.txt b/requirements.txt
index 1c56f845..6a95af5b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,7 +1,7 @@
 numpy
 scipy
 pandas
-matplotlib<=3.5.3
+matplotlib
 cartopy
 obspy
 pyproj
diff --git a/requirements.yml b/requirements.yml
index 1dd4d9ab..14caee7e 100644
--- a/requirements.yml
+++ b/requirements.yml
@@ -7,7 +7,7 @@ dependencies:
   - numpy
   - pandas
   - scipy
-  - matplotlib<=3.5.3
+  - matplotlib
   - pyproj
   - obspy
   - python-dateutil
diff --git a/setup.py b/setup.py
index 9edc6fd3..5390de9f 100644
--- a/setup.py
+++ b/setup.py
@@ -30,7 +30,7 @@ def get_version():
         'numpy',
         'scipy',
         'pandas',
-        'matplotlib<=3.5.3',
+        'matplotlib',
         'cartopy',
         'obspy',
         'pyproj',

From 7142fbbf4fa75cc64bf2fb6786b0eeac99037b80 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 15 Nov 2022 11:06:48 -0800
Subject: [PATCH 25/29] style: updated comment formats in binomial evaluations
 style: changed variable names in simulation function to keep it consistent
 style: updated named of tests in test_evaluations.py to better reflect the
 test

---
 csep/core/binomial_evaluations.py | 68 +++++++++++++------------------
 tests/test_evaluations.py         |  4 +-
 2 files changed, 30 insertions(+), 42 deletions(-)

diff --git a/csep/core/binomial_evaluations.py b/csep/core/binomial_evaluations.py
index 0c9346b6..6984bd2f 100644
--- a/csep/core/binomial_evaluations.py
+++ b/csep/core/binomial_evaluations.py
@@ -87,42 +87,40 @@ def binary_joint_log_likelihood_ndarray(forecast, catalog):
                     An Observation has to be Number of Events in Each Bin
                     It has to be a either zero or positive integer only (No Floating Point)
     """
-    #First, we mask the forecast in cells where we could find log=0.0 singularities:
+    # First, we mask the forecast in cells where we could find log=0.0 singularities:
     forecast_masked = numpy.ma.masked_where(forecast.ravel() <= 0.0, forecast.ravel())
-    
-    #Then, we compute the log-likelihood of observing one or more events given a Poisson distribution, i.e., 1 - Pr(0) 
+    # Then, we compute the log-likelihood of observing one or more events given a Poisson distribution, i.e., 1 - Pr(0)
     target_idx = numpy.nonzero(catalog.ravel())
     y = numpy.zeros(forecast_masked.ravel().shape)
     y[target_idx[0]] = 1
     first_term = y * (numpy.log(1.0 - numpy.exp(-forecast_masked.ravel())))
-    
-    #Also, we estimate the log-likelihood in cells no events are observed:
+    # Also, we estimate the log-likelihood in cells no events are observed:
     second_term = (1-y) * (-forecast_masked.ravel().data)
-    #Finally, we sum both terms to compute the joint log-likelihood score:
+    # Finally, we sum both terms to compute the joint log-likelihood score:
     return sum(first_term.data + second_term.data)
     
     
-def _simulate_catalog(num_events, sampling_weights, sim_fore, random_numbers=None):
-
-    # generate uniformly distributed random numbers in [0,1), this
+def _simulate_catalog(sim_cells, sampling_weights, sim_fore, random_numbers=None):
+    # Modified this code to generate simulations in a way that every cell gets one earthquake
+    # Generate uniformly distributed random numbers in [0,1), this
     if random_numbers is None:
-        random_numbers = numpy.random.rand(num_events)
-    else:
-        # TODO: ensure that random numbers are all between 0 and 1.
-        pass
-
-    # reset simulation array to zero, but don't reallocate
-    sim_fore.fill(0)
-
-    eqs = 0
-    while eqs < num_events:
+        # Reset simulation array to zero, but don't reallocate
+        sim_fore.fill(0)
+        num_active_cells = 0
+        while num_active_cells < sim_cells:
             random_num = numpy.random.uniform(0,1)
-            loc = numpy.searchsorted(sampling_weights, random_num)
+            loc = numpy.searchsorted(sampling_weights, random_num, side='right')
             if sim_fore[loc] == 0:
-                numpy.add.at(sim_fore, loc, 1)
-                eqs = eqs+1
-    
-    return sim_fore    
+               sim_fore[loc] = 1
+               num_active_cells = num_active_cells + 1
+    else:
+        # Find insertion points using binary search inserting to satisfy a[i-1] <= v < a[i]
+        pnts = numpy.searchsorted(sampling_weights, random_numbers, side='right')
+        # Create simulated catalog by adding to the original locations
+        numpy.add.at(sim_fore, pnts, 1)
+
+    assert sim_fore.sum() == sim_cells, "simulated the wrong number of events!"
+    return sim_fore
     
 
 def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000, random_numbers=None, 
@@ -152,28 +150,20 @@ def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000,
     # data structures to store results
     sim_fore = numpy.zeros(sampling_weights.shape)
     simulated_ll = []
-    n_obs = len(np.unique(np.nonzero(observed_data.ravel())))
+    n_active_cells = len(np.unique(np.nonzero(observed_data.ravel())))
     n_fore = numpy.sum(forecast_data)
-    expected_forecast_count = int(n_obs) 
-    
-    if use_observed_counts and normalize_likelihood:
-        scale = n_obs / n_fore
-        expected_forecast_count = int(n_obs)
-        forecast_data = scale * forecast_data
+    expected_forecast_count = int(n_active_cells)
 
     # main simulation step in this loop
     for idx in range(num_simulations):
         if use_observed_counts:
-            num_events_to_simulate = int(n_obs)
-        else:
-            num_events_to_simulate = int(numpy.random.poisson(expected_forecast_count))
+            num_cells_to_simulate = int(n_active_cells)
     
         if random_numbers is None:
-            sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore)
+            sim_fore = _simulate_catalog(num_cells_to_simulate, sampling_weights, sim_fore)
         else:
-            sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore,
+            sim_fore = _simulate_catalog(num_cells_to_simulate, sampling_weights, sim_fore,
                                          random_numbers=random_numbers[idx,:])
-
     
         # compute joint log-likelihood
         current_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, sim_fore)
@@ -185,8 +175,6 @@ def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000,
         if verbose:
             if (idx + 1) % 100 == 0:
                 print(f'... {idx + 1} catalogs simulated.')
-                
-                target_idx = numpy.nonzero(catalog.ravel())
 
     # observed joint log-likelihood
     obs_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, observed_data)
@@ -354,7 +342,7 @@ def binary_paired_t_test(forecast, benchmark_forecast, observed_catalog, alpha=0
     """ Computes the binary t-test for gridded earthquake forecasts.
 
     This score is positively oriented, meaning that positive values of the information gain indicate that the
-    forecast is performing better than the benchmark forecast.
+    forecast is performing better than the benchmark forecast
 
     Args:
         forecast (csep.core.forecasts.GriddedForecast): nd-array storing gridded rates, axis=-1 should be the magnitude column
diff --git a/tests/test_evaluations.py b/tests/test_evaluations.py
index ffc6f3ce..3f45e749 100644
--- a/tests/test_evaluations.py
+++ b/tests/test_evaluations.py
@@ -24,7 +24,7 @@ def __init__(self, *args, **kwargs):
 
     def test_simulate_catalog(self):
         # expecting the sampling weights to be [0.25, 0.5, 0.75, 1.0]
-        # assuming the random numbers are equal to thhe following:
+        # assuming the random numbers are equal to the following:
         random_numbers = numpy.array([[0.5488135, 0.71518937, 0.60276338, 0.54488318]])
 
         num_events = 4
@@ -80,7 +80,7 @@ def __init__(self, *args, **kwargs):
         self.forecast_data = numpy.array([[0.1, 0.3, 0.4], [0.2, 0.1, 0.1]])
         self.observed_data = numpy.array([[0, 1, 2], [1, 1, 0]])
 
-    def test_likelihood(self):
+    def test_joint_likelihood_calculation(self):
         bill = binary_joint_log_likelihood_ndarray(self.forecast_data, self.observed_data)
 
         numpy.testing.assert_allclose(bill, -6.7197988064)

From 985aad8165e96000435c91e450d05f8f8a6176f1 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Mon, 14 Nov 2022 11:35:47 -0800
Subject: [PATCH 26/29] Updated docstrings in catalogs.py Added verbose option
 to get_event_counts() Added additional test case to CatalogForecast creation

---
 csep/core/catalogs.py  | 17 +++++++++++------
 csep/core/forecasts.py | 12 +++++++++---
 tests/test_forecast.py | 19 ++++++++++++++++++-
 3 files changed, 38 insertions(+), 10 deletions(-)

diff --git a/csep/core/catalogs.py b/csep/core/catalogs.py
index 25603ad8..3b0fecfe 100644
--- a/csep/core/catalogs.py
+++ b/csep/core/catalogs.py
@@ -737,16 +737,16 @@ def spatial_magnitude_counts(self, mag_bins=None, tol=0.00001):
         """ Return counts of events in space-magnitude region.
 
         We figure out the index of the polygons and create a map that relates the spatial coordinate in the
-        Cartesian grid with with the polygon in region.
+        Cartesian grid with the polygon in region.
 
         Args:
-            mag_bins: magnitude bins (optional). tries to use magnitue bins associated with region
+            mag_bins (list, numpy.array): magnitude bins (optional), if empty tries to use magnitude bins associated with region
+            tol (float): tolerance for comparisons within magnitude bins
 
         Returns:
             output: unnormalized event count in each bin, 1d ndarray where index corresponds to midpoints
 
         """
-
         # make sure region is specified with catalog
         if self.region is None:
             raise CSEPCatalogException("Cannot create binned rates without region information.")
@@ -784,8 +784,8 @@ def get_bvalue(self, mag_bins=None, return_error=True):
         If that fails, uses the default magnitude bins provided in constants.
 
         Args:
-            reterr (bool): returns errors
             mag_bins (list or array_like): monotonically increasing set of magnitude bin edges
+            return_error (bool): returns errors
 
         Returns:
             bval (float): b-value
@@ -824,6 +824,10 @@ def p():
         else:
             return bval
 
+    def b_positive(self):
+        """ Implements the b-positive indicator from Nicholas van der Elst """
+        pass
+
     def plot(self, ax=None, show=False, extent=None, set_global=False, plot_args=None):
         """ Plot catalog according to plate-carree projection
 
@@ -1028,9 +1032,10 @@ def read_catalog_line(line):
                         raise ValueError(
                             "catalog_id should be monotonically increasing and events should be ordered by catalog_id")
                 # yield final catalog, note: since this is just loading catalogs, it has no idea how many should be there
-                yield cls(data=events, catalog_id=prev_id, **kwargs)
+                cat = cls(data=events, catalog_id=prev_id, **kwargs)
+                yield cat
 
-        if os.path.isdir(filename):
+        elif os.path.isdir(filename):
             raise NotImplementedError("reading from directory or batched files not implemented yet!")
 
     @classmethod
diff --git a/csep/core/forecasts.py b/csep/core/forecasts.py
index 68cf27e7..4b2f863f 100644
--- a/csep/core/forecasts.py
+++ b/csep/core/forecasts.py
@@ -649,7 +649,7 @@ def magnitude_counts(self):
             self.get_expected_rates()
         return self.expected_rates.magnitude_counts()
 
-    def get_event_counts(self):
+    def get_event_counts(self, verbose=True):
         """ Returns a numpy array containing the number of event counts for each catalog.
 
             Note: This function can take a while to compute if called without already iterating through a forecast that
@@ -661,7 +661,13 @@ def get_event_counts(self):
         """
         if len(self._event_counts) == 0:
             # event counts is filled while iterating over the catalog
-            for _ in self:
+            t0 = time.time()
+            for i, _ in enumerate(self):
+                if verbose:
+                    tens_exp = numpy.floor(numpy.log10(i + 1))
+                    if (i + 1) % 10 ** tens_exp == 0:
+                        t1 = time.time()
+                        print(f'Processed {i + 1} catalogs in {t1 - t0:.2f} seconds', flush=True)
                 pass
         return numpy.array(self._event_counts)
 
@@ -697,7 +703,7 @@ def get_expected_rates(self, verbose=False):
                     tens_exp = numpy.floor(numpy.log10(i + 1))
                     if (i + 1) % 10 ** tens_exp == 0:
                         t1 = time.time()
-                        print(f'Processed {i + 1} catalogs in {t1 - t0} seconds', flush=True)
+                        print(f'Processed {i + 1} catalogs in {t1 - t0:.3f} seconds', flush=True)
             # after we iterate through the catalogs, we know self.n_cat
             data = data / self.n_cat
             self.expected_rates = GriddedForecast(self.start_time, self.end_time, data=data, region=self.region,
diff --git a/tests/test_forecast.py b/tests/test_forecast.py
index f63d8a3e..7b427586 100644
--- a/tests/test_forecast.py
+++ b/tests/test_forecast.py
@@ -1,14 +1,24 @@
-import os, unittest
+import os
+import unittest
 import numpy
 from csep import load_catalog_forecast
 
+
 def get_test_catalog_root():
     root_dir = os.path.dirname(os.path.abspath(__file__))
     data_dir = os.path.join(root_dir, 'artifacts', 'test_ascii_catalogs')
     return data_dir
 
+
 class TestCatalogForecastCreation(unittest.TestCase):
 
+    def test_all_present(self):
+        fname = os.path.join(get_test_catalog_root(), 'all_present.csv')
+        test_fore = load_catalog_forecast(fname)
+        total_event_count = numpy.array([cat.event_count for cat in test_fore]).sum()
+        self.assertEqual(10, test_fore.n_cat)
+        self.assertEqual(10, total_event_count)
+
     def test_ascii_load_all_empty(self):
         fname = os.path.join(get_test_catalog_root(), 'all_empty.csv')
         test_fore = load_catalog_forecast(fname)
@@ -56,5 +66,12 @@ def test_get_event_counts(self):
         test_fore = load_catalog_forecast(fname)
         numpy.testing.assert_array_equal(numpy.ones(10), test_fore.get_event_counts())
 
+    def test_multiple_iterations(self):
+        fname = os.path.join(get_test_catalog_root(), 'all_present.csv')
+        test_fore = load_catalog_forecast(fname)
+        ec1 = [cat.event_count for cat in test_fore]
+        ec2 = [cat.event_count for cat in test_fore]
+        numpy.testing.assert_array_equal(ec1, ec2)
+
 if __name__ == '__main__':
     unittest.main()

From 09e2769730153196329b651ad74c713ee995ac21 Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Tue, 15 Nov 2022 11:09:28 -0800
Subject: [PATCH 27/29] style: updated variable names to better reflect the
 binomial evaluation style: changed names of functions in test_evaluations.py

---
 csep/core/binomial_evaluations.py | 50 ++++++++++++++++++-------------
 tests/test_evaluations.py         |  4 ++-
 2 files changed, 32 insertions(+), 22 deletions(-)

diff --git a/csep/core/binomial_evaluations.py b/csep/core/binomial_evaluations.py
index 0c9346b6..60f0468f 100644
--- a/csep/core/binomial_evaluations.py
+++ b/csep/core/binomial_evaluations.py
@@ -5,6 +5,7 @@
 from csep.models import EvaluationResult
 from csep.core.exceptions import CSEPCatalogException
 
+
 def _nbd_number_test_ndarray(fore_cnt, obs_cnt, variance, epsilon=1e-6):
     """ Computes delta1 and delta2 values from the Negative Binomial (NBD) number test.
 
@@ -87,24 +88,24 @@ def binary_joint_log_likelihood_ndarray(forecast, catalog):
                     An Observation has to be Number of Events in Each Bin
                     It has to be a either zero or positive integer only (No Floating Point)
     """
-    #First, we mask the forecast in cells where we could find log=0.0 singularities:
+    # First, we mask the forecast in cells where we could find log=0.0 singularities:
     forecast_masked = numpy.ma.masked_where(forecast.ravel() <= 0.0, forecast.ravel())
     
-    #Then, we compute the log-likelihood of observing one or more events given a Poisson distribution, i.e., 1 - Pr(0) 
+    # Then, we compute the log-likelihood of observing one or more events given a Poisson distribution, i.e., 1 - Pr(0)
     target_idx = numpy.nonzero(catalog.ravel())
     y = numpy.zeros(forecast_masked.ravel().shape)
     y[target_idx[0]] = 1
     first_term = y * (numpy.log(1.0 - numpy.exp(-forecast_masked.ravel())))
     
-    #Also, we estimate the log-likelihood in cells no events are observed:
+    # Also, we estimate the log-likelihood in cells no events are observed:
     second_term = (1-y) * (-forecast_masked.ravel().data)
-    #Finally, we sum both terms to compute the joint log-likelihood score:
+    # Finally, we sum both terms to compute the joint log-likelihood score:
     return sum(first_term.data + second_term.data)
     
     
 def _simulate_catalog(num_events, sampling_weights, sim_fore, random_numbers=None):
 
-    # generate uniformly distributed random numbers in [0,1), this
+    # Generate uniformly distributed random numbers in [0,1)
     if random_numbers is None:
         random_numbers = numpy.random.rand(num_events)
     else:
@@ -116,7 +117,7 @@ def _simulate_catalog(num_events, sampling_weights, sim_fore, random_numbers=Non
 
     eqs = 0
     while eqs < num_events:
-            random_num = numpy.random.uniform(0,1)
+            random_num = numpy.random.uniform(0, 1)
             loc = numpy.searchsorted(sampling_weights, random_num)
             if sim_fore[loc] == 0:
                 numpy.add.at(sim_fore, loc, 1)
@@ -152,7 +153,7 @@ def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000,
     # data structures to store results
     sim_fore = numpy.zeros(sampling_weights.shape)
     simulated_ll = []
-    n_obs = len(np.unique(np.nonzero(observed_data.ravel())))
+    n_obs = len(numpy.unique(numpy.nonzero(observed_data.ravel())))
     n_fore = numpy.sum(forecast_data)
     expected_forecast_count = int(n_obs) 
     
@@ -172,9 +173,8 @@ def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000,
             sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore)
         else:
             sim_fore = _simulate_catalog(num_events_to_simulate, sampling_weights, sim_fore,
-                                         random_numbers=random_numbers[idx,:])
+                                         random_numbers=random_numbers[idx, :])
 
-    
         # compute joint log-likelihood
         current_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, sim_fore)
         
@@ -185,8 +185,6 @@ def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000,
         if verbose:
             if (idx + 1) % 100 == 0:
                 print(f'... {idx + 1} catalogs simulated.')
-                
-                target_idx = numpy.nonzero(catalog.ravel())
 
     # observed joint log-likelihood
     obs_ll = binary_joint_log_likelihood_ndarray(forecast_data.data, observed_data)
@@ -220,12 +218,16 @@ def binary_spatial_test(gridded_forecast, observed_catalog, num_simulations=1000
     gridded_catalog_data = observed_catalog.spatial_counts()
 
     # simply call likelihood test on catalog data and forecast
-    qs, obs_ll, simulated_ll = _binary_likelihood_test(gridded_forecast.spatial_counts(), gridded_catalog_data,
-                                                        num_simulations=num_simulations,
-                                                        seed=seed,
-                                                        random_numbers=random_numbers,
-                                                        use_observed_counts=True,
-                                                        verbose=verbose, normalize_likelihood=True)
+    qs, obs_ll, simulated_ll = _binary_likelihood_test(
+        gridded_forecast.spatial_counts(),
+        gridded_catalog_data,
+        num_simulations=num_simulations,
+        seed=seed,
+        random_numbers=random_numbers,
+        use_observed_counts=True,
+        verbose=verbose,
+        normalize_likelihood=True
+    )
 
     
 # populate result data structure
@@ -273,10 +275,16 @@ def binary_conditional_likelihood_test(gridded_forecast, observed_catalog, num_s
     gridded_catalog_data = observed_catalog.spatial_magnitude_counts()
 
     # simply call likelihood test on catalog data and forecast
-    qs, obs_ll, simulated_ll = _binary_likelihood_test(gridded_forecast.data, gridded_catalog_data,
-                                                        num_simulations=num_simulations, seed=seed, random_numbers=random_numbers,
-                                                        use_observed_counts=True,
-                                                        verbose=verbose, normalize_likelihood=False)
+    qs, obs_ll, simulated_ll = _binary_likelihood_test(
+        gridded_forecast.data,
+        gridded_catalog_data,
+        num_simulations=num_simulations,
+        seed=seed,
+        random_numbers=random_numbers,
+        use_observed_counts=True,
+        verbose=verbose,
+        normalize_likelihood=False
+    )
 
     # populate result data structure
     result = EvaluationResult()
diff --git a/tests/test_evaluations.py b/tests/test_evaluations.py
index ffc6f3ce..025e7425 100644
--- a/tests/test_evaluations.py
+++ b/tests/test_evaluations.py
@@ -11,6 +11,7 @@ def get_datadir():
     data_dir = os.path.join(root_dir, 'artifacts', 'Comcat')
     return data_dir
 
+
 class TestPoissonLikelihood(unittest.TestCase):
 
     def __init__(self, *args, **kwargs):
@@ -85,5 +86,6 @@ def test_likelihood(self):
 
         numpy.testing.assert_allclose(bill, -6.7197988064)
 
+
 if __name__ == '__main__':
-    unittest.main()
\ No newline at end of file
+    unittest.main()

From 53bbd1a97d3f5ff94feea94fde4fcd836612d374 Mon Sep 17 00:00:00 2001
From: khawajasim <asimkhawaja786@gmail.com>
Date: Mon, 12 Dec 2022 22:28:43 +0100
Subject: [PATCH 28/29] unit test for sim_cat (#209)

* testing_likelihood
* name correction
* fixing imports
---
 csep/core/binomial_evaluations.py |  2 +-
 tests/test_evaluations.py         | 42 +++++++++++++++++++++++++------
 2 files changed, 36 insertions(+), 8 deletions(-)

diff --git a/csep/core/binomial_evaluations.py b/csep/core/binomial_evaluations.py
index ab97f793..58fd7f50 100644
--- a/csep/core/binomial_evaluations.py
+++ b/csep/core/binomial_evaluations.py
@@ -152,7 +152,7 @@ def _binary_likelihood_test(forecast_data, observed_data, num_simulations=1000,
     # data structures to store results
     sim_fore = numpy.zeros(sampling_weights.shape)
     simulated_ll = []
-    n_active_cells = len(np.unique(np.nonzero(observed_data.ravel())))
+    n_active_cells = len(numpy.unique(numpy.nonzero(observed_data.ravel())))
     n_fore = numpy.sum(forecast_data)
     expected_forecast_count = int(n_active_cells)
 
diff --git a/tests/test_evaluations.py b/tests/test_evaluations.py
index 71557478..c7468528 100644
--- a/tests/test_evaluations.py
+++ b/tests/test_evaluations.py
@@ -2,9 +2,8 @@
 import numpy
 import unittest
 
-from csep.core.poisson_evaluations import _simulate_catalog, _poisson_likelihood_test
-from csep.core.binomial_evaluations import binary_joint_log_likelihood_ndarray
-
+import csep.core.poisson_evaluations as poisson
+import csep.core.binomial_evaluations as binary
 
 def get_datadir():
     root_dir = os.path.dirname(os.path.abspath(__file__))
@@ -48,21 +47,21 @@ def test_simulate_catalog(self):
 
         # this is taken from the test likelihood function
         sim_fore = numpy.empty(sampling_weights.shape)
-        sim_fore = _simulate_catalog(num_events, sampling_weights, sim_fore,
+        sim_fore = poisson._simulate_catalog(num_events, sampling_weights, sim_fore,
                                      random_numbers=self.random_matrix)
 
         # final statement
         numpy.testing.assert_allclose(expected_catalog, sim_fore)
 
         # test again to ensure that fill works properply
-        sim_fore = _simulate_catalog(num_events, sampling_weights, sim_fore,
+        sim_fore = poisson._simulate_catalog(num_events, sampling_weights, sim_fore,
                                      random_numbers=self.random_matrix)
 
         # final statement
         numpy.testing.assert_allclose(expected_catalog, sim_fore)
 
     def test_likelihood(self):
-        qs, obs_ll, simulated_ll = _poisson_likelihood_test(self.forecast_data, self.observed_data, num_simulations=1,
+        qs, obs_ll, simulated_ll = poisson._poisson_likelihood_test(self.forecast_data, self.observed_data, num_simulations=1,
                                                             random_numbers=self.random_matrix, use_observed_counts=True)
 
         # very basic result to pass "laugh" test
@@ -78,13 +77,42 @@ def test_likelihood(self):
 class TestBinomialLikelihood(unittest.TestCase):
     def __init__(self, *args, **kwargs):
         super().__init__(*args, **kwargs)
+        self.seed = 0
+        numpy.random.seed(self.seed)
         self.forecast_data = numpy.array([[0.1, 0.3, 0.4], [0.2, 0.1, 0.1]])
         self.observed_data = numpy.array([[0, 1, 2], [1, 1, 0]])
+        self.random_matrix = numpy.random.rand(1, 9)
 
     def test_joint_likelihood_calculation(self):
-        bill = binary_joint_log_likelihood_ndarray(self.forecast_data, self.observed_data)
+        bill = binary.binary_joint_log_likelihood_ndarray(self.forecast_data, self.observed_data)
+        numpy.testing.assert_allclose(bill, -6.7197988064)
 
+    def test_simulate_active_cells(self):
+        #With fixed seed we get the same random numbers if we get all the number at once or one by one.
+        #Making sure random number generated by seed 0 match.
+        expected_random_numbers = numpy.array([[0.5488135, 0.71518937, 0.60276338, 0.54488318, 0.4236548, 0.64589411,
+                             0.4375872112626925, 0.8917730007820798, 0.9636627605010293]])
+
+        numpy.testing.assert_allclose(expected_random_numbers, self.random_matrix)
+
+        #We can expect the following catalog, if we get the above random numbers.
+        #We get 4 active cells after 9th random sample.
+        expected_catalog = [0, 0, 1, 1, 1, 1]
+
+        sampling_weights = numpy.cumsum(self.forecast_data.ravel()) / numpy.sum(self.forecast_data)
+        sim_fore = numpy.zeros(sampling_weights.shape)
+        obs_active_cells =  len(numpy.unique(numpy.nonzero(self.observed_data.ravel())))
+        #resetting seed again to 0, to make sure _simulate_catalog uses this.
+        seed = 0
+        numpy.random.seed(seed)
+        sim_fore = binary._simulate_catalog(obs_active_cells, sampling_weights, sim_fore)
+        numpy.testing.assert_allclose(expected_catalog, sim_fore)
+
+    def test_binomial_likelihood(self):
+        qs, bill, simulated_ll = binary._binary_likelihood_test(self.forecast_data,self.observed_data, num_simulations=1,seed=0, verbose=True)
         numpy.testing.assert_allclose(bill, -6.7197988064)
+        numpy.testing.assert_allclose(qs, 1)
+        numpy.testing.assert_allclose(simulated_ll[0], -7.921741654647629)
 
 
 if __name__ == '__main__':

From 8010dbc65a4358ee16b3e00bddba2db6a1c24d3c Mon Sep 17 00:00:00 2001
From: William <wsavran@usc.edu>
Date: Mon, 12 Dec 2022 14:33:36 -0800
Subject: [PATCH 29/29] bumped version numbers

---
 CHANGELOG.md     | 24 +++++++++++++++++++++++-
 CITATION.cff     |  2 +-
 codemeta.json    |  4 ++--
 csep/_version.py |  2 +-
 4 files changed, 27 insertions(+), 5 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index f3057973..f82f1d50 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,7 +1,29 @@
+# v0.6.1 (12/12/2022)
+
+# Change-log
+Added quadtree csv reader ([#186](https://github.com/SCECcode/pycsep/pull/186))  
+Non-Poissonian tests
+([#189](https://github.com/SCECcode/pycsep/pull/189),
+[#205](https://github.com/SCECcode/pycsep/pull/205),
+[#208](https://github.com/SCECcode/pycsep/pull/208),
+[#209](https://github.com/SCECcode/pycsep/pull/209))  
+Added plots for p-values, and confidence ranges for consistency tests ([#190](https://github.com/SCECcode/pycsep/pull/190))    
+Added NZ testing and collection regions ([#198](https://github.com/SCECcode/pycsep/pull/198))  
+Fixed region border plotting issue ([#199](https://github.com/SCECcode/pycsep/pull/199))  
+Added documentation for non-Poissonian tests ([#202](https://github.com/SCECcode/pycsep/pull/202))  
+Support for BSI catalog ([#201](https://github.com/SCECcode/pycsep/pull/201))  
+Fixed compatibility with new version of matplotlib ([#206](https://github.com/SCECcode/pycsep/pull/206))
+
+## Credits
+Pablo Iturrieta (@pabloitu)  
+Jose Bayona (@bayonato89)  
+Khawaja Asim (@khawajasim)  
+William Savran (@wsavran)
+
 # v0.6.0 (02/04/2022)
 
 ## Change-log
-Adds support for quadtree regions [#184](https://github.com/SCECcode/pycsep/pull/184)
+Adds support for quadtree regions ([#184])(https://github.com/SCECcode/pycsep/pull/184)
 
 ## Credits
 Khawaja Asim (@khawajasim)  
diff --git a/CITATION.cff b/CITATION.cff
index 670b50d9..5b01f9cd 100644
--- a/CITATION.cff
+++ b/CITATION.cff
@@ -14,6 +14,6 @@ authors:
     given-names: Philip J.
     orcid: 0000-0002-9221-7068
 title: "pyCSEP - Tools for Earthquake Forecast Developers"
-version: 0.4.1
+version: 0.6.1
 repository: https://github.com/SCECcode/pycsep
 date-released: 2021-04-20 
diff --git a/codemeta.json b/codemeta.json
index 31301e2c..c8f61d30 100644
--- a/codemeta.json
+++ b/codemeta.json
@@ -9,7 +9,7 @@
     "downloadUrl": "https://github.com/SCECcode/pycsep",
     "issueTracker": "https://github.com/SCECcode/pycsep/issues",
     "name": "pyCSEP",
-    "version": "v0.6.0",
+    "version": "v0.6.1",
     "description": "The pyCSEP Toolkit helps earthquake forecast model developers evaluate their forecasts with the goal of understanding earthquake predictability.",
     "applicationCategory": "Seismology",
     "developmentStatus": "active",
@@ -30,7 +30,7 @@
         "NumPy 1.21.3 or later (https://numpy.org)",
         "SciPy 1.7.1 or later (https://scipy.org)",
         "pandas 1.3.4 or later (https://pandas.pydata.org)",
-        "cartopy 0.20.0 or later (https://scitools.org.uk/cartopy/docs/latest)",
+        "cartopy 0.21.5 or later (https://scitools.org.uk/cartopy/docs/latest)",
         "GEOS 3.7.2 or later (https://trac.osgeo.org/geos/)",
         "PROJ 8.0.0 or later (https://proj.org/)"
     ],
diff --git a/csep/_version.py b/csep/_version.py
index d07e93fd..37416fa9 100644
--- a/csep/_version.py
+++ b/csep/_version.py
@@ -1,2 +1,2 @@
-__version__ = "0.6.0"
+__version__ = "0.6.1"