Variance reduction for Markov chains with application to MCMC

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.

Variance reduction via empirical variance minimization: convergence and complexity

In this paper we propose and study a generic variance reduction approach. The proposed method is based on minimization of the empirical variance over a suitable class of zero mean control functionals. We discuss several possibilities of constructing zero mean control functionals and present the corresponding convergence analysis. Finally, a simulation study showing the numerical efficiency of the proposed approach is presented.