Difference-Based Causal Models: Bridging the gap between Granger causality and DCMs

In recent years, the study of causality in the brain, or effective connectivity, has become increasingly important in the field of computational neuroscience. Neuroimaging modalities such as EEG, fMRI and MEG provide an immense and rich source of data. Causal analysis has the potential to help make sense of this complex data, and provide important insights about the neural basis of cognition. Two of the predominant methods for this task are Granger causality [Granger, 1969] and Dynamic Causal Modeling (DCM) [Friston et al., 2003]. Stated simply, DCM is the practice of modeling neurological activation with a set of continuous-time differential equations and using data to fit the coupling parameters of the model. By contrast, Granger causality is a more exploratory method which seeks to explain the variance of variables at time t by conditioning on other variables at times τ < t.