Paul Jenkins (University of Warwick) (webinar)

“Asymptotic genealogies of interacting particle systems”

Abstract: Interacting particle systems are a broad class of stochastic models for phenomena arising in physics, engineering, biology, and finance. A prominent class of such models can be expressed as a sequential Monte Carlo algorithm in which the aim is to construct an empirical approximation to a sequence of measures. The approximation is constructed by evolving a discrete-time, weighted population of particles, alternating between a Markov update and a resampling step. Resampling gives rise to a notion of a genealogy in which duplicated particles are regarded as offspring of their parents. 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 sequential Monte Carlo and an evolving biological population. This is joint work with Suzie Brown, Adam Johansen, Jere Koskela, and Dario Spanò.