Parallel marginalization Monte Carlo with applications to conditional path sampling

TL;DR

This paper introduces a parallel marginalization Monte Carlo method that leverages coarse Markov chains to reduce correlation times, improving efficiency in sampling from complex distributions, with demonstrated success in stochastic differential equation applications.

Contribution

The paper presents a novel parallel marginalization approach that uses auxiliary coarse chains and exchanges to enhance Monte Carlo sampling efficiency.

Findings

Effective in reducing correlation times in sampling.

Successful application to bridge sampling problems.

Improved performance in stochastic differential equation filtering.

Abstract

Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty. The method utilizes information from rapidly equilibrating coarse Markov chains that sample marginal distributions of the full system. This is accomplished through exchanges between the full chain and the auxiliary coarse chains. Results of numerical tests on the bridge sampling and filtering/smoothing problems for a stochastic differential equation are presented.