Quantitative approximations of evolving probability measures and sequential Markov Chain Monte Carlo methods

TL;DR

This paper develops non-asymptotic error bounds for particle system approximations of evolving probability measures, with applications to sequential MCMC methods in high-dimensional settings.

Contribution

It introduces explicit error bounds for interacting particle systems combining Markov moves and resampling, applicable to high-dimensional problems.

Findings

Derived non-asymptotic error bounds with explicit constants.

Applied bounds to high-dimensional product measures.

Demonstrated relevance to sequential MCMC for Monte Carlo integration.

Abstract

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation.