Particle filter with rejection control and unbiased estimator of the marginal likelihood

TL;DR

This paper introduces a particle filter method combining resampling and rejection control that provides unbiased estimates of the marginal likelihood, crucial for model comparison and reliable inference.

Contribution

It presents a novel particle filter with rejection control that achieves unbiased estimation of the marginal likelihood, addressing a gap in existing methods.

Findings

Enables unbiased estimation of the marginal likelihood.

Improves model comparison and confidence interval computation.

Applicable in particle MCMC and other exact approximation methods.

Abstract

We consider the combined use of resampling and partial rejection control in sequential Monte Carlo methods, also known as particle filters. While the variance reducing properties of rejection control are known, there has not been (to the best of our knowledge) any work on unbiased estimation of the marginal likelihood (also known as the model evidence or the normalizing constant) in this type of particle filter. Being able to estimate the marginal likelihood without bias is highly relevant for model comparison, computation of interpretable and reliable confidence intervals, and in exact approximation methods, such as particle Markov chain Monte Carlo. In the paper we present a particle filter with rejection control that enables unbiased estimation of the marginal likelihood.