Dynamic causal modeling and Granger causality Comments on: The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution

“These authors and a related commentary (Friston, 2009) concluded that: i) The concepts of temporal precedence and G-causality should not be used in fMRI connectivity analysis (Roebroeck et al. 2011-this issue).” First, I should say this was not the conclusion I wanted to convey. Second, I apologize for the superficial and dismissive treatment of Granger causality in Friston (2009): I was asked to provide a ‘primer’ that focused specifically on the implications of David et al. (2009) for non-specialists. This focus precluded a balanced discussion of effective connectivity analyses. In contrast, Roebroeck et al. (2011-this issue) provide a comprehensive and compelling treatment of the essential issues; while companion papers (in this section) offer a wider discussion on some of the conceptual and technical issues. In light of these papers, I will limit my comments on Roebroeck et al. to develop or nuance some of the key points they make. The reservations articulated in Friston (2009) were not about temporal precedence but about the vector autoregressive models (VAR) on which G-causal inference is based. These reservations are technical and formal: Technically, Granger causal analysis (GCA) rests on the theory of Martingales, which requires random fluctuations in the brain to be infinitely ‘rough’ (like white noise). Pedro Valdes Sosa and I (Valdes-Sosa and Friston, 2011) discuss the implications of this elsewhere. The formal reservations are based on the form of VAR or linear stochastic models (LSM), reviewed nicely in Roebroeck et al. These forms can preclude an interpretation of the model parameters in terms of directed connectivity; I deal with this below but start by commenting on two key themes Roebroeck et al. highlight.