Paul Jenkins: Asymptotic genealogies of interacting particle systems
Time: Thu 2019-09-12 15.15
Location: Room F11, Lindstedtsvägen 22
Lecturer: Paul Jenkins, University of Warwick
Abstract: Interacting particle systems are a broad class of stochastic models for phenomena in disciplines including physics, engineering, biology, and finance. A prominent example in statistics is the particle filter, which features prominently in numerical approximation schemes for observations from hidden Markov models. A particle filter proceeds by evolving a discrete-time, weighted population of particles whose empirical measure approximates the distribution of the hidden process. In this talk I discuss how to characterise the genealogy underlying this evolving particle system. More precisely, under certain conditions we can show that the genealogy converges (as the number of particles grows) to Kingman's coalescent, a stochastic tree-valued process widely studied in population genetics. This makes explicit the analogy between a particle filter and an evolving biological population.