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April 2010 Batch means and spectral variance estimators in Markov chain Monte Carlo
James M. Flegal, Galin L. Jones
Ann. Statist. 38(2): 1034-1070 (April 2010). DOI: 10.1214/09-AOS735

Abstract

Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic normal distribution. We consider spectral and batch means methods for estimating this variance. In particular, we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort increases. In addition, for the batch means and overlapping batch means methods we establish conditions ensuring consistency in the mean-square sense which in turn allows us to calculate the optimal batch size up to a constant of proportionality. Finally, we examine the empirical finite-sample properties of spectral variance and batch means estimators and provide recommendations for practitioners.

Citation

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James M. Flegal. Galin L. Jones. "Batch means and spectral variance estimators in Markov chain Monte Carlo." Ann. Statist. 38 (2) 1034 - 1070, April 2010. https://doi.org/10.1214/09-AOS735

Information

Published: April 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1184.62161
MathSciNet: MR2604704
Digital Object Identifier: 10.1214/09-AOS735

Subjects:
Primary: 60J22
Secondary: 62M15

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 2 • April 2010
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