Title: Asymptotic genealogies of SMC methods
Authors: Jere Koskela - University of Warwick (United Kingdom) [presenting]
Paul Jenkins - University of Warwick (United Kingdom)
Adam Johansen - University of Warwick (United Kingdom)
Dario Spano - University of Warwick (United Kingdom)
Abstract: It is well known that the genealogy embedded into an SMC algorithm by resampling plays a central role in important questions, such as estimation of variances of SMC estimators, and mixing of conditional SMC schemes. Nevertheless, results on the distribution of genealogies have only been available in the toy setting of particle filters with constant importance weights, in which case genealogies of finite samples of particles converge to the Kingman coalescent in the large ensemble size limit. We will show that the same convergence holds under verifiable assumptions which are typically satisfied by real SMC algorithms on compact state spaces, present a connection between genealogies and effective sample size, and discuss implications for SMC storage cost and variance estimation.