On the asymptotic variance of reversible Markov chain without cycles

Chi-Hao Wu; Ting-Li Chen

doi:10.1016/j.spl.2018.01.020

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arXiv · 1712.03808

On the asymptotic variance of reversible Markov chain without cycles

Chi-Hao Wu·Ting-Li Chen

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Abstract

Markov chain Monte Carlo(MCMC) is a popular approach to sample from high dimensional distributions, and the asymptotic variance is a commonly used criterion to evaluate the performance. While most popular MCMC algorithms are reversible, there is a growing literature on the development and analyses of nonreversible MCMC. Chen and Hwang(2013) showed that a reversible MCMC can be improved by adding an antisymmetric perturbation. They also raised a conjecture that it can not be improved if there is no cycle in the corresponding graph. In this paper, we present a rigorous proof of this conjecture. The proof is based on the fact that the transition matrix with an acyclic structure will produce minimum commute time between vertices.

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Chi-Hao Wu, Ting-Li Chen. 2017-12-11. On the asymptotic variance of reversible Markov chain without cycles. https://doi.org/10.1016/j.spl.2018.01.020

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