Zeng, ZijianLi, MengVannucci, Marina2024-07-252024-07-252024Zeng, Z., Li, M., & Vannucci, M. (2024). Bayesian Image-on-Scalar Regression with a Spatial Global-Local Spike-and-Slab Prior. Bayesian Analysis, 19(1), 235–260. https://doi.org/10.1214/22-BA1352https://hdl.handle.net/1911/117487In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart process prior to handle within-image dependency, and propose a general global-local spatial selection prior that broadly relates to a rich class of well-studied selection priors. Unlike existing constructions, we achieve simultaneous global (i.e., at covariate-level) and local (i.e., at pixel/voxel-level) selection by introducing participation rate parameters that measure the probability for the individual covariates to affect the observed images. This along with a hard-thresholding strategy leads to dependency between selections at the two levels, introduces extra sparsity at the local level, and allows the global selection to be informed by the local selection, all in a model-based manner. We design an efficient Gibbs sampler that allows inference for large image data. We show on simulated data that parameters are interpretable and lead to efficient selection. Finally, we demonstrate performance of the proposed model by using data from the Autism Brain Imaging Data Exchange (ABIDE) study (Di Martino et al., 2014).engExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license.  Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Journal article22-BA1352https://doi.org/10.1214/22-BA1352