Markov Chain Monte Carlo in Practice

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Abstract

Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of probability distributions commonly encountered in modern applications. For MCMC simulation to produce reliable outcomes, it needs to generate observations representative of the target distribution, and it must be long enough so that the errors of Monte Carlo estimates are small. We review methods for assessing the reliability of the simulation effort, with an emphasis on those most useful in practically relevant settings. Both strengths and weaknesses of these methods are discussed. The methods are illustrated in several examples and in a detailed case study.

Original languageEnglish (US)
Pages (from-to)557-578
Number of pages22
JournalAnnual Review of Statistics and Its Application
Volume9
DOIs
StatePublished - Mar 2022

Bibliographical note

Funding Information:
The authors thank Austin Brown and Dootika Vats for helpful comments on an early draft. They thank an anonymous reviewer for helpful suggestions. Jones was partially supported by the National Science Foundation.

Publisher Copyright:
© 2022 Annual Reviews Inc.. All rights reserved.

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