Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations

TL;DR

This paper introduces a simple, adaptive algorithm for dynamically selecting temperature ladders in parallel tempering MCMC, significantly improving sampling efficiency on complex, multi-modal distributions in astrophysical inference.

Contribution

The paper proposes a novel, easy-to-implement method for dynamically adjusting temperature spacings in parallel tempering, enhancing sampling efficiency over traditional fixed configurations.

Findings

Efficiency gains of 1.2-2.5 times over geometric temperature configurations.

Adaptive temperature spacing improves exchange acceptance ratios.

The method outperforms non-adaptive approaches across various test problems.

Abstract

Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform poorly on strongly multi-modal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve more efficient sampling, as measured by the autocorrelation time of the sampler. In particular, we present a simple, easily-implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling. This algorithm dynamically adjusts the temperature spacing to achieve a uniform rate of exchanges between chains at neighbouring temperatures. We compare the algorithm to conventional geometric temperature configurations on a number of test distributions and on an astrophysical inference problem, reporting efficiency gains by a factor of 1.2-2.5 over a well-chosen geometric temperature configuration and by a factor of 1.5-5 over a poorly chosen configuration. On all of these problems a sampler using the dynamical adaptations to achieve uniform acceptance ratios between neighbouring chains outperforms one that does not.