Chopin, Nicolas; Singh, Sumeetpal S.; Soto, Tomás; Vihola, Matti On resampling schemes for particle filters with weakly informative observations. (English) Zbl 1517.65010 Ann. Stat. 50, No. 6, 3197-3222 (2022). Summary: 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. Cited in 1 Document MSC: 65C35 Stochastic particle methods 65C05 Monte Carlo methods 60J25 Continuous-time Markov processes on general state spaces Keywords:Feynman-Kac model; hidden Markov model; particle filter; path integral; resampling Software:Quicksort; Julia × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link HAL References: [1] Andrieu, C., Doucet, A. and Holenstein, R. (2010). Particle Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 269-342. · Zbl 1411.65020 · doi:10.1111/j.1467-9868.2009.00736.x [2] ARNAUDON, M. and DEL MORAL, P. (2020). A duality formula and a particle Gibbs sampler for continuous time Feynman-Kac measures on path spaces. Electron. J. 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