# Markov Chain Monte Carlo

Publication year: 2012
Source: Exploring Monte Carlo Methods, 2012, Pages 133-169

William L., Dunn , J. Kenneth, Shultis

Summary: Markov chains are defined and their relation to transition matrices and kernels are described. Markov chain Monte Carlo (MCMC) employs the Metropolis-Hastings (MH) algorithm as another sampling mechanism. The utility of MCMC is that it can be used to sample complex PDFs, even if the normalization constants are unknown. It is shown that the MH process necessarily leads to the reversibility of the transition function. The myth of burn-in to obtain proper samples is discussed and multidimensional sampling is discussed. The Gibbs sampler is introduced as a special case of the MH algorithm. Then Bayesian probability concepts are introduced along…