Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Particle filters for partially-observed diffusions.
AU - Fearnhead, Paul
AU - Papaspiliopoulos, O.
AU - Roberts, Gareth O.
N1 - This is a pre-print of an article published in Journal of the Royal Statistical Society, Series B, 70 (4), 2008. (c) Wiley.
PY - 2008/9
Y1 - 2008/9
N2 - 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.
AB - 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.
KW - Continuous-time particle filtering
KW - Exact Algorithm
KW - Auxiliary Variables
KW - Central Limit Theorem
KW - Cox Process
U2 - 10.1111/j.1467-9868.2008.00661.x
DO - 10.1111/j.1467-9868.2008.00661.x
M3 - Journal article
VL - 70
SP - 755
EP - 777
JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)
JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)
SN - 1369-7412
IS - 4
ER -