Batch-Size Selection of Batch Means and Spectral Variance Estimators in Markov Chain Monte Carlo

• Activity Number: 664
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:30 AM
• Sponsor: IMS
• Author(s): Ying Liu* and James Flegal
• Companies: University of California at Riverside and University of California at Riverside
• Keywords: Markov chain Monte Carlo ; Monte Carlo standard error ; Batch mean ; Spectral variance estimator ; Batch size

Abstract

Markov chain Monte Carlo algorithms are used to estimate expectations when independent sampling is difficult. Monte Carlo standard error (MCSE) is important to assessing the quality of the MCMC estimate. Existing methods to estimate MCSE such as batch means estimator and spectral variance estimator require a choice of batch size which largely influences the finite sample performances of the estimators. One way to select an optimal batch size is to minimize the mean squared error of the estimator, therefore variance and bias of the estimator are of interest. We present the expression of variance for spectral variance estimator and discuss how it may contribute to the batch size selection for spectral variance estimator. Some other methods to choose the batch size of MCSE estimators will be mentioned as well and we will illustrate how the choice of the batch size affect the estimate of MCSE.