Abstract
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. Key Words: Gibbs samplingMarkov chain Monte CarloMultivariate density simulationReversible Markov chains
Keywords
Metropolis–Hastings algorithmGibbs samplingMarkov chain Monte CarloAlgorithmMarkov chainComputer scienceRejection samplingSampling (signal processing)MathematicsHybrid Monte CarloArtificial intelligenceMachine learningBayesian probability
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Publication Info
- Year
- 1995
- Type
- article
- Volume
- 49
- Issue
- 4
- Pages
- 327-335
- Citations
- 3632
- Access
- Closed
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Cite This
Siddhartha Chib,
Edward Greenberg
(1995).
Understanding the Metropolis-Hastings Algorithm.
The American Statistician
, 49
(4)
, 327-335.
https://doi.org/10.1080/00031305.1995.10476177
Identifiers
- DOI
- 10.1080/00031305.1995.10476177