Particle filters for partially observed diffusions
Particle filters for partially observed diffusions
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DOI：
10.1111/j.1467-9868.2008.00661.x
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发表时间：
2008-01-01
影响因子：
5.8
通讯作者：
Roberts, Gareth O.
中科院分区：
文献类型：
--
作者：
Fearnhead, Paul;Papaspiliopoulos, Omiros;Roberts, Gareth O.
针对一类部分观测的多元扩散，提出了一种新的粒子滤波方案。我们考虑了多种观测方案，包括带误差观测的扩散、多元扩散分量子集的观测和泊松过程的到达时间，泊松过程的强度是扩散的已知函数（Cox过程）。与目前可用的方法不同，我们的粒子滤波器不需要通过使用时间离散来近似过渡和/或观测密度。相反，他们建立在精确模拟扩散过程和无偏估计过渡密度的最新方法上。我们引入广义泊松估计量，它推广了Beskos等人的泊松估计量。给出了粒子滤波格式的中心极限定理。
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.