PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Particle filters for partially observed diffusions
Omiros Papaspiliopoulos, Gareth Roberts and Paul Fearnhead
Journal of the Royal Statistical Society, series B 2008.


We introduce a novel particle filter scheme for a class of partially observed multivariate diffusions. We consider a variety of observation schemes, including diffusion observed with error, observation of a subset of the components of the multivariate diffusion and arrival times of a Poisson process whose intensity is a known function of the diffusion (Cox process). Unlike currently available methods, our particle filters do not require approximations of the transition and/or the observation density by using time discretizations. Instead, they build on recent methodology for the exact simulation of the diffusion process and the unbiased estimation of the transition density. We introduce the generalized Poisson estimator, which generalizes the Poisson estimator of Beskos and co-workers. A central limit theorem is given for our particle filter scheme.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:5008
Deposited By:Omiros Papaspiliopoulos
Deposited On:24 March 2009