Open Access
October 2020 Coupled conditional backward sampling particle filter
Anthony Lee, Sumeetpal S. Singh, Matti Vihola
Ann. Statist. 48(5): 3066-3089 (October 2020). DOI: 10.1214/19-AOS1922


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 Schön (2020). Unbiased estimation has many advantages, such as enabling the construction of asymptotically exact confidence intervals and straightforward parallelisation.


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Anthony Lee. Sumeetpal S. Singh. Matti Vihola. "Coupled conditional backward sampling particle filter." Ann. Statist. 48 (5) 3066 - 3089, October 2020.


Received: 1 December 2018; Revised: 1 August 2019; Published: October 2020
First available in Project Euclid: 19 September 2020

MathSciNet: MR4152635
Digital Object Identifier: 10.1214/19-AOS1922

Primary: 65C40
Secondary: 65C05 , 65C35 , 65C60

Keywords: Backward sampling , conditional particle filter , convergence rate , coupling , unbiased

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 5 • October 2020
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