Post-hoc selection of dynamic causal models

Highlights

► New (post-hoc) procedure for approximating the model evidence is applied to deterministic bilinear dynamic causal models for fMRI. ► Post-hoc procedure is based on optimising only the largest model of a set of models. ► Good agreement found between free energy bound and post-hoc approximations to the model evidence and model parameters. ► Post-hoc approach reduces computational time immensely and can be applied to any nested models.

Abstract

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.