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Fixed-Width Output Analysis for Markov Chain Monte Carlo (2005)
| Citations: | 93 - 30 self |
BibTeX
@MISC{Jones05fixed-widthoutput,
author = {Galin L. Jones and Murali Haran and Brian S. Caffo and Ronald Neath},
title = {Fixed-Width Output Analysis for Markov Chain Monte Carlo},
year = {2005}
}
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Abstract
Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages 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 a variety of examples.
Keyphrases
markov chain monte carlo fixed-width output analysis ergodic average desired quantity sufficient condition target distribution regenerative simulation confidence interval finite sample property asymptotic normal distribution fundamental question simulation output critical step correlated sample monte carlo standard error ergodic average good estimate user-specified value strong consistency
