Variance reduction for Markov chains with application to MCMC

2019/10/08 by Belomestny, D., Iosipoi, L., Moulines, E. +2
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1910.03643

Abstract

In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature is theoretically demonstrated by means of a deep non asymptotic analysis of a variance reduced functional as well as by a thorough simulation study. In particular we apply our method to various MCMC Bayesian estimation problems where it favourably compares to the existing variance reduction approaches.

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