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In this article, we propose a novel spatial global-local spike-and-slabselection prior for image-on-scalar regression. We consider a Bayesianhierarchical Gaussian process model for image smoothing, that uses a flexibleInverse-Wishart process prior to handle within-image dependency, and propose ageneral global-local spatial selection prior that extends a rich class ofwell-studied selection priors. Unlike existing constructions, we achievesimultaneous global (i.e, at covariate-level) and local (i.e., atpixel/voxel-level) selection by introducing `participation rate' parametersthat measure the probability for the individual covariates to affect theobserved images. This along with a hard-thresholding strategy leads todependency between selections at the two levels, introduces extra sparsity atthe local level, and allows the global selection to be informed by the localselection, all in a model-based manner. We design an efficient Gibbs samplerthat allows inference for large image data. We show on simulated data thatparameters are interpretable and lead to efficient selection. Finally, wedemonstrate performance of the proposed model by using data from the AutismBrain Imaging Data Exchange (ABIDE) study. To the best of our knowledge, theproposed model construction is the first in the Bayesian literature tosimultaneously achieve image smoothing, parameter estimation and a two-levelvariable selection for image-on-scalar regression.

Bayesian Image-on-Scalar Regression with a Spatial Global-Local Spike-and-Slab Prior