Statistical models for brain signals with properties that evolve across trials

Most neuroscience cognitive experiments involve repeated presentations of various stimuli across several minutes or a few hours. It has been observed that brain responses, even to the same stimulus, evolve over the course of the experiment. These changes in brain activation and connectivity are believed to be associated with learning and/or habituation. In this paper, we present two general approaches to modeling dynamic brain connectivity using electroencephalograms (EEGs) recorded across replicated trials in an experiment. The first approach is the Markovian regime-switching vector autoregressive model (MS-VAR) which treats EEGs as realizations of an underlying brain process that switches between different states both within a trial and across trials in the entire experiment. The second is the slowly evolutionary locally stationary process (SEv-LSP) which characterizes the observed EEGs as a mixture of oscillatory activities at various frequency bands. The SEv-LSP model captures the dynamic nature of the amplitudes of the band-oscillations and cross-correlations between them. The MS-VAR model is able to capture abrupt changes in the dynamics while the SEv-LSP directly gives interpretable results. Moreover, it is nonparametric and hence does not suffer from model misspecification. For both of these models, time-evolving connectivity metrics in the frequency domain are derived from the model parameters for both functional and effective connectivity. We illustrate these two models for estimating cross-trial connectivity in selective attention using EEG data from an oddball paradigm auditory experiment where the goal is to characterize the evolution of brain responses to target stimuli and to standard tones presented randomly throughout the entire experiment. The results suggest dynamic changes in connectivity patterns over trials with inter-subject variability.