Understanding the Metropolis-Hastings Algorithm

by: Siddhartha Chib, Edward Greenberg

The American Statistician, Vol. 49, No. 4. (1995), pp. 327-335.

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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.

@article{citeulike:831786, 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.}, author = {Chib, Siddhartha and Greenberg, Edward }, citeulike-article-id = {831786}, doi = {10.2307/2684568}, journal = {The American Statistician}, keywords = {algorithms, bayesian, markov-chains, methods, monte-carlo, statistics}, number = {4}, pages = {327--335}, posted-at = {2008-05-13 01:30:09}, priority = {2}, title = {Understanding the Metropolis-Hastings Algorithm}, url = {http://dx.doi.org/10.2307/2684568}, volume = {49}, year = {1995} }

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TY - JOUR ID - citeulike:831786 L3 - citeulike-article-id:831786 TI - Understanding the Metropolis-Hastings Algorithm JF - The American Statistician VL - 49 IS - 4 SP - 327 EP - 335 N2 - 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. KW - algorithms KW - bayesian KW - markov-chains KW - methods KW - monte-carlo KW - statistics AU - Chib, Siddhartha AU - Greenberg, Edward PY - 1995/// UR - http://dx.doi.org/10.2307/2684568 ER -

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