Coupled conditional backward sampling particle filter
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
Published inAnnals of Statistics
© Institute of Mathematical Statistics, 2020
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. ...
PublisherInstitute of Mathematical Statistics
Publication in research information system
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Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF; Research costs of Academy Research Fellow, AoF; Academy Research Fellow, AoF
Additional information about fundingThis work wassupported by EPSRC grant numbers EP/K032208/1, EP/R014604/1 and EP/R034710/1, and by the Alan Turing Institute under the EPSRC grant EP/N510129/1. MV was supported byAcademy of Finland grants 274740, 284513, 312605 and 315619. The authors wish to ac-knowledge CSC, IT Center for Science, Finland, for computational resources.
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