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2011•Wiley series in probability and statisticsRequires access

Markov Chain Monte Carlo

Dirk P. Kroese, Thomas Taimre, Zdravko I. Botev

Open publisher page 2 citations

Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Markov chain Monte Carlo, Gibbs sampling, Metropolis–Hastings algorithm, Rejection sampling, Markov chain, Parallel tempering, Monte Carlo method, Hybrid Monte Carlo

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