Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, WC1N 3BG, UK.
J Neurosci Methods. 2012 Jun 30;208(1):66-78. doi: 10.1016/j.jneumeth.2012.04.013. Epub 2012 May 4.
Dynamic causal modelling (DCM) was originally proposed as a hypothesis driven procedure in which a small number of neurobiologically motivated models are compared. Model comparison in this context usually proceeds by individually fitting each model to data and then approximating the corresponding model evidence with a free energy bound. However, a recent trend has emerged for comparing very large numbers of models in a more exploratory manner. This led Friston and Penny (2011) to propose a post-hoc approximation to the model evidence, which is computed by optimising only the largest (full) model of a set of models. The evidence for any (reduced) submodel is then obtained using a generalisation of the Savage-Dickey density ratio (Dickey, 1971). The benefit of this post-hoc approach is a huge reduction in the computational time required for model fitting. This is because only a single model is fitted to data, allowing a potentially huge model space to be searched relatively quickly. In this paper, we explore the relationship between the free energy bound and post-hoc approximations to the model evidence in the context of deterministic (bilinear) dynamic causal models (DCMs) for functional magnetic resonance imaging data.
动态因果建模 (DCM) 最初被提议作为一种假设驱动的程序，其中比较了少量具有神经生物学动机的模型。在这种情况下，模型比较通常是通过单独拟合每个模型到数据，然后用自由能边界来近似相应的模型证据。然而，最近出现了一种更具探索性的比较大量模型的趋势。这导致 Friston 和 Penny（2011）提出了一种事后近似模型证据的方法，该方法通过仅优化模型集中最大（完整）模型来计算。然后使用 Savage-Dickey 密度比（Dickey，1971）的推广来获得任何（简化）子模型的证据。这种事后方法的好处是大大减少了模型拟合所需的计算时间。这是因为只拟合了一个模型到数据，从而可以相对快速地搜索潜在的巨大模型空间。在本文中，我们在功能磁共振成像数据的确定性（双线性）动态因果模型 (DCM) 背景下探索了自由能边界和模型证据的事后近似之间的关系。
