Monte Carlo twisting for particle filters

TL;DR

This paper introduces a novel particle filtering method using Monte Carlo twisting, which improves accuracy in estimating statistical quantities by expanding applicability through rejection sampling and unbiased approximations, with empirical validation.

Contribution

It develops a new particle filter framework with rejection sampling and unbiased estimations, enhancing efficiency and applicability for twisted Feynman--Kac models.

Findings

Lower mean squared error in normalising constant estimates compared to traditional filters.

Improved performance with more efficient sampling methods demonstrated on a stochastic volatility model.

Analysis of acceptance rates and asymptotic variance for computational cost control.

Abstract

We consider the problem of designing efficient particle filters for twisted Feynman--Kac models. Particle filters using twisted models can deliver low error approximations of statistical quantities and such twisting functions can be learnt iteratively. Practical implementations of these algorithms are complicated by the need to (i) sample from the twisted transition dynamics, and (ii) calculate the twisted potential functions. We expand the class of applicable models using rejection sampling for (i) and unbiased approximations for (ii) using a random weight particle filter. We characterise the average acceptance rates within the particle filter in order to control the computational cost, and analyse the asymptotic variance. Empirical results show the mean squared error of the normalising constant estimate in our method is smaller than a memory-equivalent particle filter but not a computation-equivalent filter. Both comparisons are improved when more efficient sampling is possible which we demonstrate on a stochastic volatility model.