Variance reduction for Markov chains with application to MCMC

TL;DR

This paper introduces a new variance reduction method for Markov chain functionals, significantly decreasing finite sample variance in MCMC Bayesian estimation through theoretical analysis and simulation comparisons.

Contribution

It presents a novel variance reduction technique based on minimizing asymptotic variance estimates, improving finite sample performance in MCMC applications.

Findings

Significant variance reduction demonstrated in simulations

Method outperforms existing variance reduction approaches

Theoretical analysis confirms effectiveness of the approach

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.