Friston K J, Penny W
The Wellcome Department of Imaging Neuroscience, London, Queen Square, London WC1N 3BG, UK.
Neuroimage. 2003 Jul;19(3):1240-9. doi: 10.1016/s1053-8119(03)00144-7.
This technical note describes the construction of posterior probability maps that enable conditional or Bayesian inferences about regionally specific effects in neuroimaging. Posterior probability maps are images of the probability or confidence that an activation exceeds some specified threshold, given the data. Posterior probability maps (PPMs) represent a complementary alternative to statistical parametric maps (SPMs) that are used to make classical inferences. However, a key problem in Bayesian inference is the specification of appropriate priors. This problem can be finessed using empirical Bayes in which prior variances are estimated from the data, under some simple assumptions about their form. Empirical Bayes requires a hierarchical observation model, in which higher levels can be regarded as providing prior constraints on lower levels. In neuroimaging, observations of the same effect over voxels provide a natural, two-level hierarchy that enables an empirical Bayesian approach. In this note we present a brief motivation and the operational details of a simple empirical Bayesian method for computing posterior probability maps. We then compare Bayesian and classical inference through the equivalent PPMs and SPMs testing for the same effect in the same data.
本技术说明描述了后验概率图的构建，该图能够对神经成像中区域特异性效应进行条件推断或贝叶斯推断。后验概率图是给定数据时激活超过某个指定阈值的概率或置信度的图像。后验概率图（PPM）是用于进行经典推断的统计参数图（SPM）的一种补充替代方法。然而，贝叶斯推断中的一个关键问题是合适先验的设定。在对先验方差的形式做一些简单假设的情况下，使用经验贝叶斯方法可以巧妙地解决这个问题，其中先验方差是从数据中估计出来的。经验贝叶斯需要一个层次观测模型，其中较高层次可视为对较低层次提供先验约束。在神经成像中，对体素上相同效应的观测提供了一个自然的两级层次结构，从而能够采用经验贝叶斯方法。在本说明中，我们简要介绍一种用于计算后验概率图的简单经验贝叶斯方法的动机和操作细节。然后，我们通过在相同数据中对相同效应进行等效的PPM和SPM测试，比较贝叶斯推断和经典推断。
