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Markov Chain Monte Carlo (MCMC)

Statistical and Numerical Computing

  1. Katherine Barnes

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vam001.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Barnes, K. 2013. Markov Chain Monte Carlo (MCMC) . Encyclopedia of Environmetrics. 3.

Author Information

  1. University of Arizona, Tucson, AZ, USA

Publication History

  1. Published Online: 15 JAN 2013


Realistic statistical models often give rise to probability distributions that are computationally difficult to use for inference. Fortunately, we now have a collection of algorithms, known as Markov chain Monte Carlo (MCMC), that has brought many of these models within our computational reach. MCMC is a simulation technique that allows one to make (approximate) draws from complex, high dimensional probability distributions. Over the last 20 years a staggering amount of research has been done on both the theoretical and applied aspects of MCMC. This article does not intend to be a complete overview of MCMC but only hopes to get the reader started in the right direction. To this end, this article begins with a general description of the types of problems that necessitate the use of MCMC. It then introduces the fundamental algorithms and addresses some general implementation issues. Discussion of the Markov chain theory underpinning MCMC algorithms has intentionally been avoided.


  • hierarchical modeling;
  • simulation methods;
  • Bayesian Statistics;
  • Gibbs sampling;
  • Metropolis–Hastings algorithm