Nick Whiteley (University of Bristol)

Twisted Particle Filters

This talk reports on an investigation of alternative sampling laws for particle filtering algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. The focus is on the regime where the length of the data record tends to infinity.

Amongst a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different from that of standard algorithms and yet the fluctuation properties of the estimates it provides are, in some ways, dramatically different. The structure of the optimal transition suggests a new class of algorithms, which we term "twisted" particle filters, and whose properties will be discussed.