The early detection of epileptic seizures requires computing relevant statistics from multivariate data and defining a robust decision strategy as a function of these statistics that accurately detects the transition from the normal to the peri-ictal (problematic) state. We model the afflicted brain as a hidden Markov model (HMM) with two hidden clinical states (normal and peri-ictal). The output of the HMM is a statistic computed from multivariate neural measurements. A Bayesian framework is developed to analyze the a posteriori conditional probability of being in peri-ictal state given current and past output measurements. We apply this method to multichannel intracortical EEGs (iEEGs) from the thalamo-cortical ictal pathway in an epilepsy rat model. We first define the output statistic as the max singular value of a connectivity matrix computed on the EEG channels with spectral techniques Then, we estimate the HMM transition probabilities from this statistic and track the a posteriori probability of being in peri-ictal state (the information state variable). We show how the information state variable changes as a function of time and we predict a seizure when this variable becomes greater than 0.5. This Bayesian strategy significantly improves over chance level and heuristically-chosen threshold-based predictors.