09. Bayesian Analysis, Plotting and MCMC Processor
MCMC Processor is a class responsible for processing MCMC and producing validation plots.
Marginalised posterior is the standard output of MCMC. PDF is mean, Gauss indicates gaussian fit to posterior while HPD (Highest Posterior Denstiity Point). In most cases paramter posteriors are Gaussian then all 3 values would give the same result. However, the strength of MCMC is that there is no assumption about gaussiantiy and it can handle non-Gaussian parameters.
This plot helps to tell which values are excluded based on X-credible intervals
It is possible to produce 2D posteriors. They are very useful to identify if parameters are correlated or not. In this example, there are strong correlations.
This can take some time, though. There are two ways: faster (using multithreading) but requiring lots of RAM or slower but without RAM requirements. Once you obtain 2D posteriors, you can produce multiple additional plots.
Correlation matrix etc are calculated based on 2D Posteriros
TrianglePlot:
- ["Test", ["Norm_Param_0", "Norm_Param_1", "Spline_Param_0", "Spline_Param_1"]]
you can specyfy as many params as you like. But also as many combinations as you like
TrianglePlot:
- ["Test", ["Norm_Param_0", "Norm_Param_1", "Spline_Param_0", "Spline_Param_1"]]
- ["Test2", ["Norm_Param_0", "Norm_Param_1"]]
It is possible to obtain the Bayes factor for different hypothesis
BayesFactor:
# Goes as follows: ParamName Name[Model 1, Model 2], Model1[lower, upper ], Model2[lower, upper ]
- ["sin2th_23", ["LO", "UO"], [0, 0.5], [0.5, 1]]
or calculate savage Dickey, which is Bayes factor for point-like hypothesis
SavageDickey:
- ["Alpha_q3", 0.0001, [0, 1]]
ParameterEvolution:
- ["Norm_Param_0", 20]
Select parameter name and how many frames you want. The more the longer it takes so be carefull
