  The focus of this work is on spatial variable selection for scalar-on-image
regression. We propose a new class of Bayesian nonparametric models,
soft-thresholded Gaussian processes and develop the efficient posterior
computation algorithms. Theoretically, soft-thresholded Gaussian processes
provide large prior support for the spatially varying coefficients that enjoy
piecewise smoothness, sparsity and continuity, characterizing the important
features of imaging data. Also, under some mild regularity conditions, the
soft-thresholded Gaussian process leads to the posterior consistency for both
parameter estimation and variable selection for scalar-on-image regression,
even when the number of true predictors is larger than the sample size. The
proposed method is illustrated via simulations, compared numerically with
existing alternatives and applied to Electroencephalography (EEG) study of
alcoholism.
