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February 2020 Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo
Jere Koskela, Paul A. Jenkins, Adam M. Johansen, Dario Spanò
Ann. Statist. 48(1): 560-583 (February 2020). DOI: 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 infinite system size limit in the sense of finite-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.

Citation

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Jere Koskela. Paul A. Jenkins. Adam M. Johansen. Dario Spanò. "Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo." Ann. Statist. 48 (1) 560 - 583, February 2020. https://doi.org/10.1214/19-AOS1823

Information

Received: 1 April 2018; Revised: 1 January 2019; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196551
MathSciNet: MR4065174
Digital Object Identifier: 10.1214/19-AOS1823

Subjects:
Primary: 60E15
Secondary: 60G99, 62E20

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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