Decomposition Sampling applied to Parallelization of Metropolis-Hastings

TL;DR

This paper introduces a decomposition sampling algorithm that enables parallelization of the Metropolis-Hastings method by dividing the sample space into overlapping parts, allowing independent subproblem solutions and diverse sampling methods.

Contribution

It proposes a novel decomposition sampling approach for parallelizing Metropolis-Hastings, enabling independent subproblem sampling with tailored methods.

Findings

Significant speedup observed in experiments

Decreased total variation in sampling results

Effective application to volatility model calibration

Abstract

This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other and are thus well suited for parallelization. Furthermore, on each of these subproblems it is possible to use distinct and independent sampling methods. In other words, specific samplers can be designed for specific parts of the sample space. The algorithms are demonstrated on a particle marginal Metropolis-Hastings sampler applied to calibration of a volatility model and two toy examples. Significant speedup and decrease of total variation is observed in experiments.