Variance reduction for Markov chains with application to MCMC

D Belomestny (1, 2) , L Iosipoi (2) , E Moulines (3, 2, 4) , A Naumov (2) , S Samsonov (2)

1 Universitat Duisberg-Essen
2 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 XPOP - Modélisation en pharmacologie de population

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.

Domaines: Statistiques [math.ST]

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