Bayesian Parameter Estimation using Markov Chain Monte Carlo (MCMC)

by Stuart Truax

initial commit: 2020-3

This repo is a collection of jupyter notebooks for doing common Bayesian parameter estimation and posterior prediction tasks using pymc3 as the MCMC solver.

Example tasks include:

• Analysis of Variance (ANOVA) using Bayesian methods
• Estimation of parameters for Gaussian Mixture Models
• Generating posterior predictive distributions
• Performing logistic regression using Bayesian methods

In each notebooks, some toy, random data will be generated and used as input to the MCMC solver. The random input data is parameterizable, which allows the user to see the effect of varying the parameters of the random input data on the results of the Bayesian estimation. For example, in ANOVA, varying the standard deviation of the level/group distributions will affect the p-value of the hypothesis test.

Primary Requirements

• python 3.6

with the libraries:

pymc3
theano

Useful Resources

A useful compendium of methods for improving MCMC estimation results:

• https://eigenfoo.xyz/bayesian-modelling-cookbook/