Article ID Journal Published Year Pages File Type
7548378 Statistics & Probability Letters 2018 5 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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