**Title:** On resampling schemes for particle filters with weakly informative observation

**Time, Date, Location**: 11:00, Friday, 6 October, 2023, Brian Anderson Building Seminar Room

**Abstract:** 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.

Joint work with N. Chopin, T. Soto and M. Vihola DOI: 10.1214/22-AOS2222

**Bio:** Following the completion of his PhD at the University of Melbourne in 2003, Sumeetpal Singh joined the University of Cambridge, initially as a postdoctoral research associate, and then became a member of faculty in 2007. Professor Singh was appointed as the Tibra Foundation Chair in Mathematical Sciences, at the University of Wollongong, in 2022, and returned to Australia to commence the appointment in January 2023. Before moving to UOW, he was a Professor of Engineering Statistics and the Head of the Signal Processing and Communications Group in Department of Engineering at the University of Cambridge. He was also a Fellow and Director of Studies of Churchill College, and a Faculty Fellow of the Alan Turing Institute in the UK.