A1 Journal article (refereed)
Coupled conditional backward sampling particle filter (2020)

Lee, A., Singh, S. S., & Vihola, M. (2020). Coupled conditional backward sampling particle filter. Annals of Statistics, 48(5), 3066-3089. https://doi.org/10.1214/19-AOS1922

JYU authors or editors

Publication details

All authors or editors: Lee, Anthony; Singh, Sumeetpal S.; Vihola, Matti

Journal or series: Annals of Statistics

ISSN: 0090-5364

eISSN: 2168-8966

Publication year: 2020

Volume: 48

Issue number: 5

Pages range: 3066-3089

Publisher: Institute of Mathematical Statistics

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1214/19-AOS1922

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71949

Publication is parallel published: https://arxiv.org/abs/1806.05852

Abstract

The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result is based on analysis of a new coupling of two CBPFs, the coupled conditional backward sampling particle filter (CCBPF). We show that CCBPF has good stability properties in the sense that with fixed number of particles, the coupling time in terms of iterations increases only linearly with respect to the time horizon under a general (strong mixing) condition. The CCBPF is useful not only as a theoretical tool, but also as a practical method that allows for unbiased estimation of smoothing expectations, following the recent developments by Jacob, Lindsten and Schon (2020). Unbiased estimation has many advantages, such as enabling the construction of asymptotically exact confidence intervals and straightforward parallelisation.

Keywords: Monte Carlo methods; stochastic processes; Markov chains; numerical analysis

Free keywords: backward sampling; convergence rate; coupling; conditional particle filter; unbiased

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 3