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Coupled conditional backward sampling particle filter

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Lee, A 
Singh, SS 
Vihola, M 

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) per- forms 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 (to appear). Unbiased estimation has many advantages, such as enabling the construction of asymptotically exact confidence intervals and straight- forward parallelisation.

Description

Keywords

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

Journal Title

Annals of Statistics

Conference Name

Journal ISSN

0090-5364
2168-8966

Volume Title

48

Publisher

Institute of Mathematical Statistics

Rights

All rights reserved
Sponsorship
Alan Turing Institute (unknown)
Engineering and Physical Sciences Research Council (EP/K032208/1)
Engineering and Physical Sciences Research Council (EP/R014604/1)
Engineering and Physical Sciences Research Council (EP/R034710/1)