Unbiased Filtering of a Class of Partially Observed Diffusions

TL;DR

This paper introduces a Monte Carlo filtering method for partially observed diffusions that is unbiased, has finite variance, and scales efficiently across multiple processors, improving upon existing particle filter techniques.

Contribution

The authors develop a novel unbiased filtering approach combining randomization and multilevel particle filtering, scalable to many processors.

Findings

Achieves unbiased filtering estimates with finite variance.

Comparable accuracy to existing methods with increased computational cost.

Scales efficiently to multiple processors.

Abstract

In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee & Glynn (2015) along with the multilevel particle filter (MLPF) approach of Jasra et al (2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.