Markov Chain Monte Carlo Methods

In Chapter 5, we introduced the use of simulation in Bayesian inference. Rejection sampling is a general method for simulating from an arbitrary posterior distribution, but it can be difficult to set up since it requires the construction of a suitable proposal density. Importance sampling and SIR algorithms are also general-purpose algorithms, but they also require proposal densities that may be difficult to find for high-dimensional problems. In this chapter, we illustrate the use of Markov chain Monte Carlo (MCMC) algorithms in summarizing posterior distributions.