Generalised Filtering
Generalised Filtering
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DOI：
10.1155/2010/621670
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发表时间：
2010-01-01
影响因子：
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通讯作者：
Daunizeau, Jean
中科院分区：
文献类型：
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作者：
Friston, Karl J.;Stephan, Klaas;Daunizeau, Jean
我们描述了一个贝叶斯滤波方案的非线性状态空间模型在连续时间。该方案被称为广义滤波，并对隐藏状态和未知参数生成观测数据进行后验（条件）密度计算。至关重要的是，该方案在线运行，吸收数据以优化时变状态和时不变参数的条件密度。与卡尔曼和粒子平滑不同，广义滤波不需要向后传递。相对于变分方案，它不假设状态和参数之间的条件独立性。广义过滤优化了条件密度相对于模型的对数证据上的自由能约束。这种优化使用隐藏状态和参数的广义运动，在参数的运动是小的先验假设下。我们描述了该计划，目前比较评价与固定形式的变分版本，并得出结论与说明性的应用程序的非线性状态空间模型的脑成像时间序列。
We describe a Bayesian filtering scheme for nonlinear state-space models in continuous time. This scheme is called Generalised Filtering and furnishes posterior (conditional) densities on hidden states and unknown parameters generating observed data. Crucially, the scheme operates online, assimilating data to optimize the conditional density on time-varying states and time-invariant parameters. In contrast to Kalman and Particle smoothing, Generalised Filtering does not require a backwards pass. In contrast to variational schemes, it does not assume conditional independence between the states and parameters. Generalised Filtering optimises the conditional density with respect to a free-energy bound on the model's log-evidence. This optimisation uses the generalised motion of hidden states and parameters, under the prior assumption that the motion of the parameters is small. We describe the scheme, present comparative evaluations with a fixed-form variational version, and conclude with an illustrative application to a nonlinear state-space model of brain imaging time-series.