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- Title
Particle filters for partially observed diffusions.
- Authors
Fearnhead, Paul; Papaspiliopoulos, Omiros; Roberts, Gareth O.
- Abstract
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.
- Subjects
MULTIVARIATE analysis; POISSON processes; DIFFUSION processes; APPROXIMATION theory; SIMULATION methods &; models; ESTIMATION theory
- Publication
Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2008, Vol 70, Issue 4, p755
- ISSN
1369-7412
- Publication type
Article
- DOI
10.1111/j.1467-9868.2008.00661.x