Small-noise analysis and symmetrization of implicit Monte Carlo samplers

TL;DR

This paper analyzes implicit Monte Carlo samplers in small noise regimes using Laplace asymptotics and proposes a symmetrization technique that improves sampling efficiency, confirmed by computational experiments.

Contribution

It introduces a symmetrization method for implicit samplers based on small noise analysis, enhancing their performance with minimal additional cost.

Findings

Symmetrization improves sampling accuracy in small noise regimes.

Laplace asymptotic analysis provides insights into sampler behavior.

Experimental results validate the theoretical improvements.

Abstract

Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algo- rithms that leads to improved (implicit) sampling schemes at a rel- atively small additional cost. Computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.