Penny Will, Kiebel Stefan, Friston Karl
Wellcome Department of Imaging Neuroscience, University College, London WC1N 3BG, UK. wpenny,
Neuroimage. 2003 Jul;19(3):727-41. doi: 10.1016/s1053-8119(03)00071-5.
We describe a Bayesian estimation and inference procedure for fMRI time series based on the use of General Linear Models with Autoregressive (AR) error processes. We make use of the Variational Bayesian (VB) framework which approximates the true posterior density with a factorised density. The fidelity of this approximation is verified via Gibbs sampling. The VB approach provides a natural extension to previous Bayesian analyses which have used Empirical Bayes. VB has the advantage of taking into account the variability of hyperparameter estimates with little additional computational effort. Further, VB allows for automatic selection of the order of the AR process. Results are shown on simulated data and on data from an event-related fMRI experiment.
我们描述了一种基于具有自回归（AR）误差过程的一般线性模型的功能磁共振成像（fMRI）时间序列的贝叶斯估计和推断程序。我们利用变分贝叶斯（VB）框架，该框架用因式分解密度近似真实后验密度。通过吉布斯采样验证了这种近似的保真度。VB方法是对以前使用经验贝叶斯的贝叶斯分析的自然扩展。VB的优点是只需很少的额外计算量就能考虑超参数估计的变异性。此外，VB允许自动选择AR过程的阶数。在模拟数据和来自事件相关fMRI实验的数据上展示了结果。
