BATCH MEANS AND SPECTRAL VARIANCE ESTIMATORS IN MARKOV CHAIN MONTE CARLO

• 成果类型: Article
• 署名作者: Flegal, James M.; Jones, Galin L.
• 署名单位: University of California System; University of California Riverside; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS735
• 发表日期: 2010
• 页码: 1034-1070
• 关键词: width output analysis; partial sums; geometric ergodicity; convergence-rates; strong consistency; gibbs samplers; simulation; approximation

摘要

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.