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December 2022 On resampling schemes for particle filters with weakly informative observations
Nicolas Chopin, Sumeetpal S. Singh, Tomás Soto, Matti Vihola
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Ann. Statist. 50(6): 3197-3222 (December 2022). DOI: 10.1214/22-AOS2222


We consider particle filters with weakly informative observations (or ‘potentials’) relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous-time Feynman–Kac path integral models—a scenario that naturally arises when addressing filtering and smoothing problems in continuous time—but our findings are indicative about weakly informative settings beyond this context too. We study the performance of different resampling schemes, such as systematic resampling, SSP (Srinivasan sampling process) and stratified resampling, as the time-discretisation becomes finer and also identify their continuous-time limit, which is expressed as a suitably defined ‘infinitesimal generator.’ By contrasting these generators, we find that (certain modifications of) systematic and SSP resampling ‘dominate’ stratified and independent ‘killing’ resampling in terms of their limiting overall resampling rate. The reduced intensity of resampling manifests itself in lower variance in our numerical experiment. This efficiency result, through an ordering of the resampling rate, is new to the literature. The second major contribution of this work concerns the analysis of the limiting behaviour of the entire population of particles of the particle filter as the time discretisation becomes finer. We provide the first proof, under general conditions, that the particle approximation of the discretised continuous-time Feynman–Kac path integral models converges to a (uniformly weighted) continuous-time particle system.

Funding Statement

TS and MV were supported by Academy of Finland grant 315619 and the Finnish Centre of Excellence in Randomness and Structures.


The authors wish to acknowledge CSC—IT Center for Science, Finland, for computational resources.


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Nicolas Chopin. Sumeetpal S. Singh. Tomás Soto. Matti Vihola. "On resampling schemes for particle filters with weakly informative observations." Ann. Statist. 50 (6) 3197 - 3222, December 2022.


Received: 1 March 2022; Revised: 1 July 2022; Published: December 2022
First available in Project Euclid: 21 December 2022

Digital Object Identifier: 10.1214/22-AOS2222

Primary: 65C35
Secondary: 60J25 , 65C05 , 65C60

Keywords: Feynman–Kac model , Hidden Markov model , particle filter , path integral , Resampling

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 6 • December 2022
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