February 2023 Multilevel bootstrap particle filter
Kari Heine, Daniel Burrows
Author Affiliations +
Bernoulli 29(1): 551-579 (February 2023). DOI: 10.3150/22-BEJ1468

Abstract

We consider situations where the applicability of sequential Monte Carlo particle filters is compromised due to the expensive evaluation of the particle weights. To alleviate this problem, we propose a new particle filter algorithm based on the multilevel approach. We show that the resulting multilevel bootstrap particle filter (MLBPF) retains the strong law of large numbers as well as the central limit theorem of classical particle filters under mild conditions. Our numerical experiments demonstrate up to 85% reduction in computation time compared to the classical bootstrap particle filter, in certain settings. While it should be acknowledged that this reduction is highly application dependent, and a similar gain should not be expected for all applications across the board, we believe that this substantial improvement in certain settings makes MLBPF an important addition to the family of sequential Monte Carlo methods.

Acknowledgements

The authors would like to thank Schlumberger Cambridge Research Limited for the financial support for this research. The second author was also supported by EPSRC grant EP/S515279/1.

Citation

Download Citation

Kari Heine. Daniel Burrows. "Multilevel bootstrap particle filter." Bernoulli 29 (1) 551 - 579, February 2023. https://doi.org/10.3150/22-BEJ1468

Information

Received: 1 April 2021; Published: February 2023
First available in Project Euclid: 13 October 2022

MathSciNet: MR4497258
zbMATH: 07634403
Digital Object Identifier: 10.3150/22-BEJ1468

Keywords: Hidden Markov model , multilevel , particle filter , sequential Monte Carlo

Vol.29 • No. 1 • February 2023
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