Optimistic Estimation of Convergence in Markov Chains with the Average-Mixing Time
Statistics Theory
2026-02-06 v4 Probability
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2402.10506,
title = {Optimistic Estimation of Convergence in Markov Chains with the Average-Mixing Time},
author = {Geoffrey Wolfer and Pierre Alquier},
journal= {arXiv preprint arXiv:2402.10506},
year = {2026}
}