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We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to electrophysiological recordings from the brain to infer crossfrequency coupling. The current metrics used to quantify the cross-frequency coupling in neuroscience cannot detect if two frequency components in non-Gaussian brain recordings are statistically independent or not. Our MI-in-frequency metric, based on Shannon's mutual information between the Cramér's representation of stochastic processes, overcomes this shortcoming and can detect statistical dependence in frequency between non-Gaussian signals. We then describe two data-driven estimators of MI-in-frequency: one based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated data. We then use MI-in-frequency to estimate mutual information between two data streams that are dependent across time, without making any parametric model assumptions. Finally, we use the MI-infrequency metric to investigate the cross-frequency coupling in seizure onset zone from electrocorticographic recordings during seizures. The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.

Epilepsy is a dynamic disease in which the brain transitions between different states. In this paper, we focus on the problem of identifying the time points, referred to as change points, where the transitions between these different states happen. A Bayesian change point detection algorithm that does not require the knowledge of the total number of states or the parameters of the probability distribution modeling the activity of epileptic brain in each of these states is developed in this paper. This algorithm works in online mode making it amenable for real-time monitoring. To reduce the quadratic complexity of this algorithm, an approximate algorithm with linear complexity in the number of data points is also developed. Finally, we use these algorithms on ECoG recordings of an epileptic patient to locate the change points and determine segments corresponding to different brain states.

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