Description
Describe the issue:
Hi developers,
I have analytically found the second derivative of following posterior at MAP of 2/3 to be 0.15713. The likelihood is simply Binomial with a Uniform prior on [0, 1]. I can get the exact analytical value from an older version like 4.0.0 but in the new version it returns 0.64!
Pr \left( p \vert W, L \right) &= 840 p^6 \left( 1- p \right)^3
Reproduceable code example:
import numpy as np
import pymc as pm
data = np.repeat((0, 1), (3, 6))
with pm.Model() as normal_approximation:
p = pm.Uniform("p", 0, 1) # uniform priors
w = pm.Binomial("w", n=len(data), p=p, observed=data.sum()) # binomial likelihood
mean_q = pm.find_MAP()
p_value = normal_approximation.rvs_to_values[p]
p_value.tag.transform = None
p_value.name = p.name
std_q = ((1 / pm.find_hessian(mean_q, vars=[p])) ** 0.5)[0]
# display summary of quadratic approximation
print("Mean, Standard deviation\np {:.2}, {:.2}".format(mean_q["p"], std_q[0]))Error message:
No response
PyMC version information:
pymc 5.10.3 hd8ed1ab_0 conda-forge
pymc-base 5.10.3 pyhd8ed1ab_0 conda-forge
pyparsing 3.1.1 pyhd8ed1ab_0 conda-forge
pytensor 2.18.4 py310hc6cd4ac_0 conda-forge
pytensor-base 2.18.4 py310hcc13569_0 conda-forge
python 3.10.13 hd12c33a_1_cpython conda-forge
Running on linux through WSL2 (windows 11)
environment created through conda from conda-forge channel
Context for the issue:
I encountered this issue for the statistical rethinking course. You can refer to the code 2.6 in the provided notebook.
https://github.com/pymc-devs/pymc-resources/blob/main/Rethinking_2/Chp_02.ipynb