Introduction

MCMC Processor is a class responsible for processing MCMC and producing validation plots.

Posteriors

Marginalised posterior is the standard output of MCMC. PDF is mean, Gauss indicates Gaussian fit to posterior while HPD (Highest Posterior Density Point). In most cases parameter 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 will all be produced when running ProcessMCMC.

Parameter Plot

This plot is summarising 1D posteriors in more compact way. It is being printed by default.

Since these plots are often targeted for publication, there is a tool called GetPosftitParams which make this plot with ability group parameter in whatever fashion you like. You can read more here

Credible Intervals

This plot helps to tell which values are excluded based on X-credible intervals

To produce, make sure the following field is true.

ProcessMCMC:

MakeCredibleIntervals: true

2D Posteriors

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.

To enable, this option must be on.

ProcessMCMC:

PlotCorr: true

Threshold

Not every 2D plot will be made. MaCh3 uses configurable threshold to print only more interesting plot. Threshold applies to correlation factor.

ProcessMCMC:

Post2DPlotThreshold: 0.2

Credible Region

ProcessMCMC:
  PlotCorr: true
  MakeCredibleRegions: true

Correlation Matrix

Correlation matrix etc are calculated based on 2D Posteriors

Triangle plot

TrianglePlot:

- ["Test", ["Norm_Param_0", "Norm_Param_1", "Spline_Param_0", "Spline_Param_1"]]

You can specify as many parameters 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"]]

Violin plot

ProcessMCMC:
  PlotCorr: true
  MakeViolin: true

Bayes factor and Savage-Dickey

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]]

Parameter Evolution

ParameterEvolution:

- ["Norm_Param_0", 20]

Select parameter name and how many frames you want. The more, the longer it takes, so be careful

Bipolar plot

Ridgeline plot

Reweighting

TODO!!!