Markov Chain Monte Carlo Sampling
Emmanuel M. E. H. Lesaffre, Andrew B Lawson · 2012
This chapter explores an attractive class of sampling algorithms, called Markov chain Monte Carlo (MCMC) methods. The two most important MCMC procedures are (a) the Gibbs sampler and (b) the Metropolis (—Hastings) (MH) algorithm. It is the introduction of these two sampling algorithms that revolutionized Bayesian statistics and created an immense revival of the Bayesian idea by offering solutions to practical problems. MCMC techniques allow for tackling statistical modeling problems which are hard (or even impossible) to solve with maximum likelihood procedures, thereby offering the applied statistician a rich toolbox of statistical modeling techniques. The justification of the MCMC approaches, that is, why they give a sample from the posterior distribution, is treated in the chapter. Controlled Vocabulary Terms Bayesian statistics; Gibbs sampling; Markov chain Monte Carlo methods; Metropolis-Hastings algorithm