  Patients with epilepsy can manifest short, sub-clinical epileptic "bursts" in
addition to full-blown clinical seizures. We believe the relationship between
these two classes of events---something not previously studied
quantitatively---could yield important insights into the nature and intrinsic
dynamics of seizures. A goal of our work is to parse these complex epileptic
events into distinct dynamic regimes. A challenge posed by the intracranial EEG
(iEEG) data we study is the fact that the number and placement of electrodes
can vary between patients. We develop a Bayesian nonparametric Markov switching
process that allows for (i) shared dynamic regimes between a variable number of
channels, (ii) asynchronous regime-switching, and (iii) an unknown dictionary
of dynamic regimes. We encode a sparse and changing set of dependencies between
the channels using a Markov-switching Gaussian graphical model for the
innovations process driving the channel dynamics and demonstrate the importance
of this model in parsing and out-of-sample predictions of iEEG data. We show
that our model produces intuitive state assignments that can help automate
clinical analysis of seizures and enable the comparison of sub-clinical bursts
and full clinical seizures.
