Before revision:  We demonstrate that our approach can reliably identify the direction of interaction and the corresponding delays with numerical simulations using linear stochastic systems as well as  nonlinear dynamical systems such as a network of neural mass models  . Finally, we apply our method to real-world observational microelectrode array  data from rodent brain slices to study the causal effect networks underlying epileptic activity.
After revision:  We demonstrate that our approach can reliably identify the direction of interaction and the corresponding delays with numerical simulations using linear stochastic systems as well as nonlinear dynamical systems such as a network of neural mass models ), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays . Finally, we apply our method to real-world observational microelectrode array data from rodent brain slices to study the causal effect networks underlying epileptic activity.