Rare-Event Sampling: Occupation-Based Performance Measures for Parallel Tempering and Infinite Swapping Monte Carlo Methods

TL;DR

This paper introduces rigorous performance measures for tempering-based Monte Carlo methods, demonstrating their effectiveness in rare-event sampling for Lennard-Jones clusters, with infinite swapping outperforming traditional parallel tempering.

Contribution

The paper develops new, broadly applicable performance measures for tempering-based Monte Carlo methods based on a rigorous property, improving evaluation of rare-event sampling efficiency.

Findings

Infinite swapping outperforms parallel tempering in Lennard-Jones cluster sampling.

Performance measures are rigorous, informative, and easy to implement.

The methods are applicable to a range of tempering-based Monte Carlo techniques.

Abstract

In the present paper we identify a rigorous property of a number of tempering-based Monte Carlo sampling methods, including parallel tempering as well as partial and infinite swapping. Based on this property we develop a variety of performance measures for such rare-event sampling methods that are broadly applicable, informative, and straightforward to implement. We illustrate the use of these performance measures with a series of applications involving the equilibrium properties of simple Lennard-Jones clusters, applications for which the performance levels of partial and infinite swapping approaches are found to be higher than those of conventional parallel tempering.