Variance reduction for Markov chains with application to MCMC
Statistics Theory
2020-02-18 v2 Machine Learning
Probability
Computation
Machine Learning
Statistics Theory
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.
Cite
@article{arxiv.1910.03643,
title = {Variance reduction for Markov chains with application to MCMC},
author = {D. Belomestny and L. Iosipoi and E. Moulines and A. Naumov and S. Samsonov},
journal= {arXiv preprint arXiv:1910.03643},
year = {2020}
}