Effective connectivity depends critically on state-space models with biophysically informed observation and
state equations. These models have to be endowed with priors on unknown parameters and afford checks for
model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger
Causal Modeling and other approaches. We establish links between past and current statistical causal
modeling, in terms of Bayesian dependency graphs and Wiener–Akaike–Granger–Schweder influence
measures. We show that some of the challenges faced in this field have promising solutions and speculate on
future developments.
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