Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 70, Issue -, Pages 755-777Publisher
WILEY
DOI: 10.1111/j.1467-9868.2008.00661.x
Keywords
auxiliary variables; central limit theorem; continuous time particle filtering; Cox process; exact algorithm
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Funding
- Engineering and Physical Sciences Research Council [EP/D002060/1] Funding Source: researchfish
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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.
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