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arXiv · 1910.03643

Variance reduction for Markov chains with application to MCMC

D. Belomestny·L. Iosipoi·E. Moulines·A. Naumov·S. Samsonov
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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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BibTeXRIS

D. Belomestny, L. Iosipoi, E. Moulines, A. Naumov, S. Samsonov. 2019-10-08. Variance reduction for Markov chains with application to MCMC. https://arxiv.org/abs/1910.03643

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