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 editorsLee, Anthony; Singh, Sumeetpal S.; Vihola, Matti

Journal or seriesAnnals of Statistics



Publication year2020


Issue number5

Pages range3066-3089

PublisherInstitute of Mathematical Statistics

Publication countryUnited States

Publication languageEnglish


Publication open accessNot open

Publication channel open access

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

Publication is parallel publishedhttps://arxiv.org/abs/1806.05852


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.

KeywordsMonte Carlo methodsstochastic processesMarkov chainsnumerical analysis

Free keywordsbackward sampling; convergence rate; coupling; conditional particle filter; unbiased

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Ministry reportingYes

Reporting Year2020

JUFO rating3

Last updated on 2024-22-04 at 11:52