MCMC Diagnostic Approaches

The purpose of this chapter is to illustrate some of the things that can go wrong in Markov Chain Monte Carlo (MCMC) analysis and to introduce some diagnostic tools that help identify whether the results of such an analysis can be trusted. The goal of a Bayesian MCMC analysis is to estimate the posterior distribution while skipping the integration required in the denominator of Bayes’ Theorem. The MCMC approach does this by breaking the problem into small, bite-sized pieces, allowing the posterior distribution to be built bit by bit. The main challenge, however, is that several things might go wrong in the process. Several diagnostic tests can be applied to ensure that an MCMC analysis provides an adequate estimate of the posterior distribution. Such diagnostics are required of all MCMC analyses and include tuning, burn-in, and pruning.