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Particle filters for partially observed diffusions
Author(s) -
Fearnhead Paul,
Papaspiliopoulos Omiros,
Roberts Gareth O.
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00661.x
Subject(s) - estimator , poisson distribution , multivariate statistics , mathematics , diffusion , central limit theorem , diffusion process , limit (mathematics) , particle filter , filter (signal processing) , statistical physics , mathematical analysis , computer science , statistics , physics , kalman filter , innovation diffusion , computer vision , thermodynamics , knowledge management
Summary. 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.