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摘要翻译：
本文针对一类部分观测的多元扩散问题，提出了一种新的粒子滤波算法。连续时间动态模型，其中%信号由多元扩散过程给出。我们考虑了多种观测方案，包括有误差观测的扩散，多元扩散分量子集的观测，以及强度为扩散已知函数的泊松过程（Cox过程）的到达时间。与目前可用的方法不同，我们的粒子滤波器不需要使用时间离散来近似过渡和/或观测密度。相反，它们建立在最近的方法上，用于精确模拟扩散过程和无偏估计跃迁密度，如\cite{Besk：Papa：Robe：Fear：2006}所述。特别地，我们引入了推广的Poisson估计，它推广了\cite{Besk：Papa：Robe：Fear：2006}的Poisson估计。因此，我们的滤波器避免了由%时间离散引起的系统偏差，并且与其他连续时间滤波器相比具有显著的计算优势。这些优点在理论上得到了一个中心极限定理的支持。
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英文标题：
《Particle Filters for Partially Observed Diffusions》
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作者：
Paul Fearnhead, Omiros Papaspiliopoulos and Gareth Roberts
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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英文摘要：
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %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 \cite{besk:papa:robe:fear:2006}. %In particular, w We introduce the Generalised Poisson Estimator, which generalises the Poisson Estimator of \cite{besk:papa:robe:fear: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 A central limit theorem is given for our particle filter scheme.
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PDF链接：
https://arxiv.org/pdf/710.4245
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