On the asymptotic variance of reversible Markov chain without cycles

Chi-Hao Wu and Ting-Li Chen

Statistics & Probability Letters, 2018, vol. 137, issue C, 224-228

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 cannot 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.

Keywords: Markov chain Monte Carlo; Rate of convergence; Reversibility; Asymptotic variance (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.01.020

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