Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a generic method for approximate sampling from an arbitrary distribution. The main idea is to generate a Markov chain whose limiting distribution is equal to the desired distribution. This chapter describes the most prominent MCMC algorithms, including Metropolis-Hastings algorithm, Gibbs sampler, hit-and-run sampler, shake-and-bake algorithm, Metropolis-Gibbs hybrids, multiple-try Metropolis-Hastings method, auxiliary variable samplers, and reversible-jump sampler. MCMC algorithms are frequently used in statistical data analysis, in particular in Bayesian statistics. Controlled Vocabulary Terms Bayesian statistics; Gibbs sampling; Markov chain Monte Carlo; Metropolis-Hastings algorithm; reversible-jump Markov chain Monte Carlo