Batch Size Selection for Variance Estimators in MCMC

Ying Liu (), Dootika Vats () and James M. Flegal ()
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Ying Liu: University of California
Dootika Vats: Indian Institute of Technology Kanpur
James M. Flegal: University of California

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 1, 65-93

Abstract: Abstract We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error for this class of estimators. Further, we propose a parametric technique for estimating optimal batch sizes and discuss practical issues regarding the estimating process. Vector auto-regressive, Bayesian logistic regression, and Bayesian dynamic space-time examples illustrate the quality of the estimation procedure where the proposed optimal batch sizes outperform current batch size selection methods.

Keywords: Asymptotic variance estimation; Batch size; Markov chain Monte Carlo; Overlapping batch means; 60J22; 62F15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-020-09841-7

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