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.
%0 Journal Article
%1 chib1995understanding
%A Chib, Siddhartha
%A Greenberg, Edward
%D 1995
%J The American Statistician
%K approximation bayes chib estimation hastings hm metropolis mixedtrails mtmc posterior
%N 4
%P 327-335
%R 10.1080/00031305.1995.10476177
%T Understanding the Metropolis-Hastings Algorithm
%U http://amstat.tandfonline.com/doi/abs/10.1080/00031305.1995.10476177
%V 49
%X 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{chib1995understanding,
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. },
added-at = {2016-09-16T08:10:12.000+0200},
author = {Chib, Siddhartha and Greenberg, Edward},
biburl = {https://www.bibsonomy.org/bibtex/2eca2e182789da65a9bccebd62951745e/becker},
doi = {10.1080/00031305.1995.10476177},
eprint = {http://amstat.tandfonline.com/doi/pdf/10.1080/00031305.1995.10476177},
interhash = {ec7af487b3b0d0a525972cb7a8e48647},
intrahash = {eca2e182789da65a9bccebd62951745e},
journal = {The American Statistician},
keywords = {approximation bayes chib estimation hastings hm metropolis mixedtrails mtmc posterior},
number = 4,
pages = {327-335},
timestamp = {2017-04-05T11:47:46.000+0200},
title = {Understanding the Metropolis-Hastings Algorithm},
url = {http://amstat.tandfonline.com/doi/abs/10.1080/00031305.1995.10476177},
volume = 49,
year = 1995
}