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 two examples of interacting 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.