Flegal, James M.; Jones, Galin L. Batch means and spectral variance estimators in Markov chain Monte Carlo. (English) Zbl 1184.62161 Ann. Stat. 38, No. 2, 1034-1070 (2010). Summary: 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. Cited in 78 Documents MSC: 62M15 Inference from stochastic processes and spectral analysis 60J22 Computational methods in Markov chains 65C05 Monte Carlo methods Keywords:Markov chain; Monte Carlo; spectral methods; batch means; standard errors × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Anderson, T. W. (1994). The Statistical Analysis of Time Series . Wiley, New York. · Zbl 0835.62074 [2] Bednorz, W. and Latuszyński, K. (2007). A few remarks on “Fixed-width output analysis for Markov chain Monte Carlo” by Jones et al. J. Amer. Statist. Assoc. 102 1485-1486. [3] Billingsley, P. (1995). Probability and Measure , 3rd ed. Wiley, New York. · Zbl 0822.60002 [4] Bratley, P., Fox, B. L. and Schrage, L. E. (1987). A Guide to Simulation . Springer, New York. · Zbl 0515.68070 [5] Chan, K. S. and Geyer, C. J. 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