Ensemble preconditioning for Markov chain Monte Carlo simulation

TL;DR

This paper introduces a parallel ensemble MCMC method that uses collective dynamics and local covariance information to improve sampling efficiency in high-dimensional, anisotropic problems, showing significant speedups in experiments.

Contribution

It presents a novel ensemble preconditioning approach for MCMC that stabilizes dynamics and enhances sampling in challenging high-dimensional settings.

Findings

Achieves significant speedups over alternative schemes.

Effectively stabilizes dynamics in anisotropic high-dimensional problems.

Demonstrates practical efficiency through numerical experiments.

Abstract

We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics thus providing a practical approach to difficult anisotropic sampling problems in high dimensions. Numerical experiments with model problems demonstrate that dramatic potential speedups, compared to various alternative schemes, are attainable.