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Résumé de communication

Résumé 221 :

Metropolising forward particle filtering backward simulation and Rao-Blackwellisation using multiple trajectories
Rydén, Tobias
KTH Royal Institute of Technology

Particle filters, or sequential Monte Carlo methods, are simulation-based methods for estimation of the latent states in state-space models. These methods have developed tremendously since invented almost 20 years ago, but common to all of them is a set of so-called particles that dynamically evolve in the state space as more observations become available; particles that fit observations well are duplicated to further explore the region where they are located while particles producing a poor fit are killed. The result is an estimate of the posterior distribution of the latent states given observations. In a recent seminal paper, Andrieu, Doucet and Holenstein (JRSSB, 2010) demonstrated that by combining particle filter dynamics with a Metropolis-Hastings step deciding whether to accept a proposed set of particle locations, one can remove the estimation bias arising from the finite number of particles altogether. In this talk we will discuss how this approach can be extended to the case when particle trajectories are not drawn from the ancestral tree created by the particle evolution, but by backward sampling in the corresponding trellis. We also point to the potential of using multiple simulated trajectories as a means to profit on the simplicity and speed of this peration, as opposed to the more expensive simulation of a complete particle history. Statistically, this can be nterpreted as partial Rao-Blackwellisation over the set of all backwards trajectories. Numerical examples on estimation of latent states, and parameter estimation through Monte Carlo EM, will be used to illustrate the above ideas.