ASYMPTOTIC GENEALOGIES OF INTERACTING PARTICLE SYSTEMS WITH AN APPLICATION TO SEQUENTIAL MONTE CARLO

• 成果类型: Article
• 署名作者: Koskela, Jere; Jenkins, Paul A.; Johansen, Adam M.; Spano, Dario
• 署名单位: University of Warwick; University of Warwick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1823
• 发表日期: 2020
• 页码: 560-583
• 关键词: feynman-kac; CONVERGENCE; variance; filters; THEOREM; chaos

摘要

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.