Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions

TL;DR

This paper establishes conditions ensuring rapid mixing of parallel and simulated tempering Markov chains for complex multimodal distributions, with applications to Bayesian inference and statistical mechanics.

Contribution

It provides unified sufficient conditions and spectral gap bounds that guarantee rapid mixing for both tempering methods across various models.

Findings

Rapid mixing conditions for tempering methods

Spectral gap lower bounds established

Applications to normal mixture and Ising models

Abstract

We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.