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Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo
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Koskela, Jere, Jenkins, Paul, Johansen, Adam M. and Spanò, Dario (2020) Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo. Annals of statistics, 48 (1). pp. 560-583. doi:10.1214/19-AOS1823
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Official URL: http://dx.doi.org/10.1214/19-AOS1823
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 | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Statistics |
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| Journal or Publication Title: | Annals of statistics | ||||||
| Publisher: | Inst Mathematical Statistics | ||||||
| ISSN: | 0090-5364 | ||||||
| Official Date: | 17 February 2020 | ||||||
| Dates: |
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| Volume: | 48 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 560-583 | ||||||
| DOI: | 10.1214/19-AOS1823 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| 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 | ||||||
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