The Annals of Statistics
- Ann. Statist.
- Volume 38, Number 2 (2010), 1034-1070.
Batch means and spectral variance estimators in Markov chain Monte Carlo
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.
Ann. Statist., Volume 38, Number 2 (2010), 1034-1070.
First available in Project Euclid: 19 February 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 62M15: Spectral analysis
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. https://projecteuclid.org/euclid.aos/1266586622