Keywords: Matrix covariates, MCMC, spatial correlation, spike and slab prior
With the advent of modern technologies, it is increasingly common to deal with data of multi-dimensions in various scientific fields of study. In this paper, we develop a Bayesian approach for the analysis of high-dimensional neuroimaging data. We specifically deal with EEG data, where we have a matrix of covariates corresponding to each subject from either the alcoholic or control group. The matrix covariates have a natural spatial correlation based on the locations of the brain, and temporal correlation as the measurements are taken over time. We employ a divide and conquer strategy by building multiple local Bayesian models at each time point separately. We incorporate the spatial structure through the structured spike and slab prior, which has inherent variable selection properties. The temporal structure is incorporated within the prior by learning from the local model from the previous time point. We pool the information from the local models and use a weighted average to design a prediction method. We perform some simulation studies to show the efficiency of our approach and demonstrate the local Bayesian modeling with a case study on EEG data.