Markov Chain Monte Carlo in Practice
- 7 March 2022
- journal article
- research article
- Published by Annual Reviews in Annual Review of Statistics and Its Application
- Vol. 9 (1), 557-578
- https://doi.org/10.1146/annurev-statistics-040220-090158
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. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.This publication has 96 references indexed in Scilit:
- Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and CompositionStatistical Science, 2013
- Exact sampling for intractable probability distributions via a Bernoulli factoryElectronic Journal of Statistics, 2012
- Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equationsProbability Theory and Related Fields, 2009
- Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?Statistical Science, 2008
- The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed ModelsJournal of the American Statistical Association, 1996
- Minorization Conditions and Convergence Rates for Markov Chain Monte CarloJournal of the American Statistical Association, 1995
- Regeneration in Markov Chain SamplersJournal of the American Statistical Association, 1995
- Markov Chains for Exploring Posterior DistributionsThe Annals of Statistics, 1994
- Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemesBiometrika, 1994
- Sampling-Based Approaches to Calculating Marginal DensitiesJournal of the American Statistical Association, 1990