# Understanding the Metropolis-Hastings Algorithm

**Siddhartha Chib****Edward Greenberg**

CiteWeb id: 20120000062

CiteWeb score: 3487

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.

**Understanding the Metropolis-Hastings Algorithm**" is placed in the Top 10000 of the best publications in CiteWeb. Also in the category Mathematics it is included to the Top 1000. Additionally, the publicaiton "

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Siddhartha Chib, Edward Greenberg,

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