An improved unbiased particle filter

Author:

Jasra Ajay1,Maama Mohamed1,Ombao Hernando2

Affiliation:

1. Applied Mathematics and Computational Science Program , Computer, Electrical and Mathematical Sciences and Engineering Division , King Abdullah University of Science and Technology , Thuwal , 23955-6900 , Kingdom of Saudi Arabia

2. Statistics Program , Computer, Electrical and Mathematical Sciences and Engineering Division , King Abdullah University of Science and Technology , Thuwal , 23955-6900 , Kingdom of Saudi Arabia

Abstract

Abstract In this paper, we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process, which typically leads to filtering that is subject to discretization bias. The approach in [A. Jasra, K. J. H. Law and F. Yu, Unbiased filtering of a class of partially observed diffusions, Adv. Appl. Probab. 54 (2022), 3, 661–687] establishes that, when only having access to the time discretized diffusion, it is possible to remove the discretization bias with an estimator of finite variance. We improve on this method by introducing a modified estimator based on the recent work [A. Jasra, M. Maama and H. Ombao, Antithetic multilevel particle filters, preprint (2023), https://arxiv.org/abs/2301.12371]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Statistics and Probability

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