  The human brain is a directional network system of brain regions involving
directional connectivity. Seizures are a directional network phenomenon as
abnormal neuronal activities start from a seizure onset zone (SOZ) and
propagate to otherwise healthy regions. To localize the SOZ of an epileptic
patient, clinicians use iEEG to record the patient's intracranial brain
activity in many small regions. iEEG data are high-dimensional multivariate
time series. We build a state-space multivariate autoregression (SSMAR) for
iEEG data to model the underlying directional brain network. To produce
scientifically interpretable network results, we incorporate into the SSMAR the
scientific knowledge that the underlying brain network tends to have a cluster
structure. Specifically, we assign to the SSMAR parameters a
stochastic-blockmodel-motivated prior, which reflects the cluster structure. We
develop a Bayesian framework to estimate the SSMAR, infer directional
connections, and identify clusters for the unobserved network edges. The new
method is robust to violations of model assumptions and outperforms existing
network methods. By applying the new method to an epileptic patient's iEEG
data, we reveal seizure initiation and propagation in the patient's brain
network. Our method can also accurately localize the SOZ. Overall, this paper
provides a tool to study the human brain network.
