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 favorably compares to the existing variance reduction approaches.

中文翻译：

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Markov链的方差减少及其在MCMC中的应用

在本文中，我们针对控制变量的适当类对这些函数的渐近方差的估计最小，提出了一种马尔可夫链附加功能的方差减少方法。所提出的方法的一个显着特征是其显着降低整体有限样本方差的能力。理论上，通过对方差缩减的函数进行深入的非渐近分析以及进行全面的模拟研究，可以证明此功能。特别地，我们将我们的方法应用于各种MCMC贝叶斯估计问题，与现有的方差减少方法相比，它具有优势。