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Understanding the Metropolis-Hastings Algorithm

Siddhartha Chib and Edward Greenberg
The American Statistician
Vol. 49, No. 4 (Nov., 1995), pp. 327-335
DOI: 10.2307/2684568
Stable URL: http://www.jstor.org/stable/2684568
Page Count: 9
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Understanding the Metropolis-Hastings Algorithm
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Abstract

We provide a detailed, introductory exposition of the Metropolis-Hastings algorithm, a powerful Markov chain method to simulate multivariate distributions. A simple, intuitive derivation of this method is given along with guidance on implementation. Also discussed are two applications of the algorithm, one for implementing acceptance-rejection sampling when a blanketing function is not available and the other for implementing the algorithm with block-at-a-time scans. In the latter situation, many different algorithms, including the Gibbs sampler, are shown to be special cases of the Metropolis-Hastings algorithm. The methods are illustrated with examples.

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