We develop scalar-on-image regression models when images are registered multidimensional manifolds. We propose a fast and scalable Bayes inferential procedure to estimate the image coefficient. The central idea is the combination of an Ising prior distribution, which controls a latent binary indicator map, and an intrinsic Gaussian Markov random field, which controls the smoothness of the nonzero coefficients. The model is fit using a single-site Gibbs sampler, which allows fitting within minutes for hundreds of subjects with predictor images containing thousands of locations. The code is simple and is provided in less than one page in the Appendix. We apply this method to a neuroimaging study where cognitive outcomes are regressed on measures of white matter microstructure at every voxel of the corpus callosum for hundreds of subjects.
Keywords: Binary Markov Random Field; Gaussian Markov Random Field; Markov Chain Monte Carlo.