Fixed-width output analysis for Markov chain Monte Carlo

• 成果类型: Article
• 署名作者: Jones, Galin L.; Haran, Murali; Caffo, Brian S.; Neath, Ronald
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Johns Hopkins University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214506000000492
• 发表日期: 2006
• 页码: 1537-1547
• 关键词: sequential confidence-intervals; geometric ergodicity; convergence-rates; strong consistency; gibbs samplers; partial-sums; simulation; variance; hastings; regeneration

摘要

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.