The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications.

翻译：马尔可夫链向其平稳分布的收敛速率通常通过全变差混合时间的概念进行评估。然而，这种最坏情况度量往往给出悲观的估计，且难以从观测数据中推断。本文主张采用平均混合时间作为一种更乐观且明显更易估计的替代方案。我们进一步阐明了其在从两点空间到可数空间等多种场景中的适用性，并讨论了一些实际应用意义。