Koskela, Jere, Jenkins, Paul, Johansen, Adam M. and Spanò, Dario (2019) Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo. Annals of statistics . (In Press)

	PDF WRAP-asymptotic-genealogies-interacting-particle-systems-application-sequential-Monte-Carlo-Koskela-2019.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (720Kb)
	PDF smc_genealogies.pdf - Submitted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (454Kb)

Request Changes to record.

Abstract

We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman n-coalescent in the in nite system size limit in the sense of nite-dimensional distributions. Thus, the tractable n-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height. SMC genealogies are known to be connected to algorithm performance, so that our results are likely to have applications in the design of new methods as well. Our conditions for convergence are strong, but we show by simulation that they do not appear to be necessary.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Computer Science Faculty of Science > Statistics
Journal or Publication Title:	Annals of statistics
Publisher:	Inst Mathematical Statistics
ISSN:	0090-5364
Official Date:	26 January 2019
Dates:	Date Event 26 January 2019 Accepted
Date of first compliant deposit:	28 January 2019
Status:	Peer Reviewed
Publication Status:	In Press
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Deutsche Forschungsgemeinschaft (DFG), Lloyd's Register Foundation
Grant number:	EP/HO23364/1, EP/L018497/1, BL 1105/3-2, Alan Turing Institute Programme on Data-Centric Engineering
Related URLs:	Publisher

Request changes or add full text files to a record

Repository staff actions (login required)

View Item