  The aim of this article is to infer the connectivity structures of brain
regions before and during epileptic seizure. Our contributions are fourfold.
First, we propose a 6N-dimensional stochastic differential equation for
modelling the activity of N coupled populations of neurons in the brain. This
model further develops the (single population) stochastic Jansen and Rit neural
mass model, which describes human electroencephalography (EEG) rhythms, in
particular signals with epileptic activity. Second, we construct a reliable and
efficient numerical scheme for the model simulation, extending a splitting
procedure proposed for one neural population. Third, we propose an adapted
Sequential Monte Carlo Approximate Bayesian Computation algorithm for
simulation-based inference of both the relevant real-valued model parameters as
well as the {0,1}-valued network parameters, the latter describing the coupling
directions among the N modelled neural populations. Fourth, after illustrating
and validating the proposed statistical approach on different types of
simulated data, we apply it to a set of multi-channel EEG data recorded before
and during an epileptic seizure. The real data experiments suggest, for
example, a larger activation in each neural population and a stronger
connectivity on the left brain hemisphere during seizure.
