Abstract

In this paper, we develop a novel spatial variable selection method for scalar on vector-valued image regression in a multi-group setting. Here, ‘vector-valued image’ refers to the imaging datasets that contain vector-valued information at each pixel/voxel location, such as in RGB color images, multimodal medical images, DTI imaging, etc. The focus of this work is to identify the spatial locations in the image having an important effect on the scalar outcome measure. Specifically, the overall effect of each voxel is of interest. We thus develop a novel shrinkage prior by soft-thresholding the ℓ2 norm of a latent multivariate Gaussian process. It allows us to estimate sparse and piecewise-smooth spatially varying vector-valued regression coefficient function. Motivated by the real data, we further develop a double soft-thresholding based framework when there are multiple pre-specified subgroups. For posterior inference, an efficient MCMC algorithm is developed. We compute the posterior contraction rate for parameter estimation and also establish consistency for variable selection of the proposed Bayesian model, assuming that the true regression coefficients are Holder smooth. Finally, we demonstrate the advantages of the proposed method in simulation studies and further illustrate in an ADNI dataset for modeling MMSE scores based on DTI -based vector-valued imaging markers.