Fixed-width output analysis for Markov chain Monte Carlo

Galin L. Jones, Murali Haran, Brian S. Caffo, Ronald Neath

Research output: Contribution to journalArticlepeer-review

175 Scopus citations

Abstract

Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are good estimates of the desired quantities. We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard error is a critical step in assessing the simulation output. We consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We give sufficient conditions for the strong consistency of both methods and investigate their finite-sample properties in various examples.

Original languageEnglish (US)
Pages (from-to)1537-1547
Number of pages11
JournalJournal of the American Statistical Association
Volume101
Issue number476
DOIs
StatePublished - Dec 2006

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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