On the asymptotic variance of reversible Markov chain without cycles
Probability
2018-02-06 v1
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.
Keywords
Cite
@article{arxiv.1712.03808,
title = {On the asymptotic variance of reversible Markov chain without cycles},
author = {Chi-Hao Wu and Ting-Li Chen},
journal= {arXiv preprint arXiv:1712.03808},
year = {2018}
}