An improved unbiased particle filter

Jasra Ajay (), Maama Mohamed () and Ombao Hernando ()
Additional contact information
Jasra Ajay: 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
Maama Mohamed: 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
Ombao Hernando: Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia

Monte Carlo Methods and Applications, 2024, vol. 30, issue 2, 149-162

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.

Keywords: Unbiased estimation; particle filters; diffusion processes; filtering (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2023-2024 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:30:y:2024:i:2:p:149-162:n:1002

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/mcma-2023-2024

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().