6. Markov Chain Monte Carlo

  1. Dirk P. Kroese1,
  2. Thomas Taimre1 and
  3. Zdravko I. Botev2

Published Online: 20 SEP 2011

DOI: 10.1002/9781118014967.ch6

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods

How to Cite

Kroese, D. P., Taimre, T. and Botev, Z. I. (2011) Markov Chain Monte Carlo, in Handbook of Monte Carlo Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118014967.ch6

Author Information

  1. 1

    University of Queensland

  2. 2

    Université de Montréal

Publication History

  1. Published Online: 20 SEP 2011
  2. Published Print: 28 FEB 2011

ISBN Information

Print ISBN: 9780470177938

Online ISBN: 9781118014967

SEARCH

Keywords:

  • Bayesian statistics;
  • Gibbs sampler;
  • hit-and-run sampler;
  • Markov chain Monte Carlo;
  • Metropolis-Hastings algorithm;
  • reversible-jump sampler;
  • shake-and-bake algorithm

Summary

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