Bayesian estimation of dynamical systems: An application to fMRI
Bayesian estimation of dynamical systems: An application to fMRI
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DOI：
10.1006/nimg.2001.1044
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发表时间：
2002-06-01
期刊：
影响因子：
5.7
通讯作者：
Friston, KJ
中科院分区：
文献类型：
--
作者：
Friston, KJ
本文提出了一种估计确定性动力系统参数的条件分布或后验分布的方法。该过程符合高斯-牛顿搜索的 EM 实现，以求条件密度或后验密度的最大值。在估计过程中包含先验可确保鲁棒且快速的收敛，并且由此产生的条件密度使得能够对模型参数进行贝叶斯推断。该方法使用 fMRI 研究中实验设计的原因或因素与随后的 BOLD 响应之间的血流动力学耦合的输入-状态-输出模型进行演示。该示例代表了当前功能磁共振成像分析模型的概括，该模型适应非线性并且其中参数具有明确的物理解释。其次，该方法将基于给定参数零假设的数据的可能性的经典推理扩展到给定数据的关于模型参数的更合理的推论。该推论提供了基于条件密度的置信区间。 (C) 2002 年爱思唯尔科学（美国）。
This paper presents a method for estimating the conditional or posterior distribution of the parameters of deterministic dynamical systems. The procedure conforms to an EM implementation of a Gauss-Newton search for the maximum of the conditional or posterior density. The inclusion of priors in the estimation procedure ensures robust and rapid convergence and the resulting conditional densities enable Bayesian inference about the model parameters. The method is demonstrated using an input-state-output model of the hemodynamic coupling between experimentally designed causes or factors in fMRI studies and the ensuing BOLD response. This example represents a generalization of current fMRI analysis models that accommodates nonlinearities and in which the parameters have an explicit physical interpretation. Second, the approach extends classical inference, based on the likelihood of the data given a null hypothesis about the parameters, to more plausible inferences about the parameters of the model given the data. This inference provides for confidence intervals based on the conditional density. (C) 2002 Elsevier Science (USA).