标题： 关于无环可逆马尔可夫链的渐近方差 显示英文标题

标题： On the asymptotic variance of reversible Markov chain without cycles

摘要： 马尔可夫链蒙特卡洛（MCMC）是一种用于从高维分布中抽样的流行方法，渐近方差是评估性能的常用准则。虽然大多数流行的MCMC算法是可逆的，但关于非可逆MCMC的开发和分析文献越来越多。陈和黄（2013）表明，通过添加一个反对称扰动可以改进一个可逆的MCMC。他们还提出了一个猜想，即如果对应图中没有循环，则无法改进。在本文中，我们给出了这个猜想的严格证明。该证明基于这样一个事实，即具有无环结构的转移矩阵会在顶点之间产生最小的往返时间。 显示英文摘要

摘要： 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.