RESAMPLE-MOVE Filtering with Cross-Model Jumps

Abstract

In standard sequential imputation, repeated resampling stages progressively impoverish the set of particles, by decreasing the number of distinct values represented in that set. A possible remedy is Rao-Blackwellisation (Liu and Chen 1998). Another remedy, which we discuss in this chapter, is to adopt a hybrid particle filter, which combines importance sampling/resampling (Rubin 1988, Smith and Gelfand 1992) and Markov chain iterations. An example of this class of particle filters is the RESAMPLEMOVE algorithm described in (Gilks and Berzuini 1999), in which the swarm of particles is adapted to an evolving target distribution by periodical resampling steps and through occasional Markov chain moves that lead each individual particle from its current position to a new point of the parameter space. These moves increase particle diversity. Markov chain moves had previously been introduced in particle filters (for example, (Berzuini, Best, Gilks and Larizza 1997, Liu and Chen 1998)), but rarely with the possibility of moving particles at any stage of the evolution process along any direction of the parameter space; this is, indeed, an important and innovative feature of RESAMPLE—MOVE. This allows, in particular, to prevent particle depletion along directions of the parameter space corresponding to static parameters, for example when the model contains unknown hyper-parameters, a situation which is not addressed by the usual state filtering algorithms.