The Annals of Statistics

Batch means and spectral variance estimators in Markov chain Monte Carlo

James M. Flegal and Galin L. Jones

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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.

Article information

Source
Ann. Statist. Volume 38, Number 2 (2010), 1034-1070.

Dates
First available in Project Euclid: 19 February 2010

Permanent link to this document
http://projecteuclid.org/euclid.aos/1266586622

Digital Object Identifier
doi:10.1214/09-AOS735

Mathematical Reviews number (MathSciNet)
MR2604704

Zentralblatt MATH identifier
05686527

Subjects
Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 62M15: Spectral analysis

Keywords
Markov chain Monte Carlo spectral methods batch means standard errors

Citation

Flegal, James M.; Jones, Galin L. Batch means and spectral variance estimators in Markov chain Monte Carlo. Ann. Statist. 38 (2010), no. 2, 1034--1070. doi:10.1214/09-AOS735. http://projecteuclid.org/euclid.aos/1266586622.


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