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Variance reduction for Markov chains with application to MCMC

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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https://hal.inria.fr/hal-03033158
Contributor : Eric Moulines <>
Submitted on : Tuesday, December 1, 2020 - 11:23:11 AM
Last modification on : Thursday, December 3, 2020 - 3:01:21 PM

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  • HAL Id : hal-03033158, version 1

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D Belomestny, L Iosipoi, E Moulines, A Naumov, S Samsonov. Variance reduction for Markov chains with application to MCMC. Statistics and Computing, Springer Verlag (Germany), 2020. ⟨hal-03033158⟩

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