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Keywords: Asymptotic theory, classification, Electroencephalography (EEG), generalized linear model, high dimensional, posterior consistency, sparsity
We propose a Bayesian generalized linear models for matrix-valued covariates data with shrinkage priors for estimation and variable selection in high-dimensional settings where the dimensions of the covariates increase as the sample size increases. This study is motivated by extending Bayesian approaches in a classical multivariate linear model. The proposed estimation can be applied to classifying matrix data such as images. We show that the proposed model achieves strong posterior consistency when the dimension grows at a subexponential rate with the sample size. Furthermore, we quantify the posterior contraction rate at which the posterior shrinks around the true regression coefficients. Simulation studies and an application to Electroencephalography and Leucorrhea data show the superior performance of the proposed method over the existing approaches.