Particle filters for partially-observed diffusions.

Fearnhead, Paul and Papaspiliopoulos, O. and Roberts, Gareth O. (2008) Particle filters for partially-observed diffusions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70 (4). pp. 755-777. ISSN 1369-7412

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In this paper we introduce novel particle filters for a class of partially-observed continuous-time dynamic models where the signal is given by a multivariate diffusion process. 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 using time-discretisations. Instead, they build on recent methodology for the exact simulation of the diffusion process and the unbiased estimation of the transition density as described in Beskos et al. (2006). In particular, we introduce the Generalised Poisson Estimator, which generalises the Poisson Estimator of Beskos et al. (2006). Thus, our filters avoid the systematic biases caused by time-discretisations and they have significant computational advantages over alternative continuous-time filters. These advantages are supported theoretically by a central limit theorem.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Additional Information:
This is a pre-print of an article published in Journal of the Royal Statistical Society, Series B, 70 (4), 2008. (c) Wiley.
Uncontrolled Keywords:
?? continuous-time particle filteringexact algorithmauxiliary variablescentral limit theoremcox processstatistics and probabilitystatistics, probability and uncertaintyqa mathematics ??
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Deposited On:
11 Jul 2008 08:04
Last Modified:
29 May 2024 00:42