Markov Chain Monte Carlo in Practice

被引：22

作者：

Jones, Galin L. ^{[1
]}

Qin, Qian ^{[1
]}

机构：

[1] Univ Minnesota, Sch Stat, Minneapolis, MN 55113 USA

来源：

ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION | 2022年 / 9卷

基金：

美国国家科学基金会;

关键词：

autocorrelation; central limit theorem; convergence diagnostics; effective sample size; Markov chain Monte Carlo; stopping rule; INTRACTABLE PROBABILITY-DISTRIBUTIONS; SPECTRAL VARIANCE ESTIMATORS; GEOMETRIC ERGODICITY; GIBBS SAMPLER; STRONG CONSISTENCY; CONVERGENCE-RATES; COVARIANCE STRUCTURE; OUTPUT ANALYSIS; BATCH MEANS; HASTINGS;

D O I：

10.1146/annurev-statistics-040220-090158

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：557 / 578

页数：22

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