Scalable spatio‐temporal Bayesian analysis of high‐dimensional electroencephalography data

Abstract We present a scalable Bayesian modelling approach for identifying brain regions that respond to a certain stimulus and use them to classify subjects. More specifically, we deal with multi‐subject electroencephalography (EEG) data with a binary response distinguishing between alcoholic and control groups. The covariates are matrix‐variate with measurements taken from each subject at different locations across multiple time points. EEG data have a complex structure with both spatial and temporal attributes. We use a divide‐and‐conquer strategy and build separate local models, that is, one model at each time point. We employ Bayesian variable selection approaches using a structured continuous spike‐and‐slab prior to identify the locations that respond to a certain stimulus. We incorporate the spatio‐temporal structure through a Kronecker product of the spatial and temporal correlation matrices. We develop a highly scalable estimation algorithm, using likelihood approximation, to deal with large number of parameters in the model. Variable selection is done via clustering of the locations based on their duration of activation. We use scoring rules to evaluate the prediction performance. Simulation studies demonstrate the efficiency of our scalable algorithm in terms of estimation and fast computation. We present results using our scalable approach on a case study of multi‐subject EEG data.