A Brief Tour of Bayesian Sampling Methods

Abstract

Unlike in the past, the modern Bayesian analyst has many options for approxi-mating intractable posterior distributions. This chapter briefly summarizes the class of posterior sampling methods known as Markov chain Monte Carlo, a type of dependent sampling strategy. Varieties of algorithms exist for constructing chains, and we review some of them here. Such methods are quite flexible and are now used routinely, even for relatively complicated statistical models. In addition, extensions of the algorithms have been developed for various goals. General-purpose software is currently also available to automate the construction of samplers, freeing the analyst to focus on model formulation and inference.