Jimmy Olsson

Particle approximation of smoothing functionals in general state space models with application
to maximum likelihood estimation.

Abstract:

The talk concerns the use of sequential Monte Carlo methods (often
alternatively termed as "particle filters") for smoothing in general
state space models.  A well known problem when applying the standard
sequential importance sampling technique in the smoothing mode is that
the resampling mechanism of the particle filter introduces degeneracy
of the approximation. This degeneracy will increase the variance of
the Monte Carlo estimates in an undesirable way. However, when
performing maximum likelihood estimation via the EM algorithm, all
involved functionals will be of additive form for a large subclass of
models. To cope with the problem in this case, a modification, relying
on forgetting properties of the filtering equations, of the standard
method is proposed. In this setting, the quality of the produced
estimates is investigated both theoretically and through simulations.