B0845
Title: Bayesian image-on-scalar regression with a spatial global-local spike-and-slab prior
Authors: Zijian Zeng - Rice University (United States)
Meng Li - Rice University (United States)
Marina Vannucci - Rice University (United States)
Meng Li - Rice University (United States) [presenting]
Abstract: Image-on-Scalar regression has wide-ranging applications in discovering the relationship between the image data and covariates measured on the same subjects. This remains challenging partly because of the highly complex spatial dependency in image data as well as the demand for the selection and interpretation of influential covariates at more than one level. We develop a method for simultaneous image smoothing, parameter estimation, and variable selection at both the image and pixel levels. 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 extends 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. The proposed method is demonstrated by using data from the Autism Brain Imaging Data Exchange (ABIDE) study.
