Convergence Monitoring and Adaptation for MCMC Algorithms

Abstract

The goal of this chapter is to present different monitoring methods (or diagnostics) proposed to check (for) the convergence of an MCMC algorithm when considering its output and to answer the most commonly asked question about MCMC, namely “when do we stop our MCMC algorithm?” We distinguish here between two separate notions of convergence, namely convergence to stationarity and convergence of ergodic average, in contrast with iid settings. We also discuss several types of convergence diagnostics, primarily those contained in the coda package of Plummer et al. (2006), even though more accurate methods may be available in specific settings.

“Why does he insist that we must have a diagnosis? Some things are not meant to be known by man.”

Susanna Gregory

An Unholy Alliance