IngentaConnect Fixed-Width Output Analysis for Markov Chain Monte Carlo

Authors: Jones, Galin L.¹; Haran, Murali²; Caffo, Brian S.³; Neath, Ronald¹

Source: Journal of the American Statistical Association, Volume 101, Number 476, December 2006 , pp. 1537-1547(11)

Publisher: American Statistical Association

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.

Keywords: BATCH MEANS; GEOMETRIC ERGODICITY; MARKOV CHAIN; MONTE CARLO CENTRAL LIMIT THEOREM; REGENERATION

Document Type: Research article

DOI: 10.1198/016214506000000492

Affiliations: 1: School of Statistics, University of Minnesota, Minneapolis, MN 55455 2: Department of Statistics, Pennsylvania State University, University Park, PA 16802 3: Department of Biostatistics, Johns Hopkins University, Baltimore, MD 21205

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