A Spatial Shrinkage Prior for Sparse Signal Detection

Abstract

Sparse signal detection in imaging data has been widely studied. However, there are remaining uncertainties and methodological challenges in relaxing the assumption of identical and independent parameters. We propose a spatial shrinkage prior motivated by the horseshoe estimator. The introduced prior allows correlation among parameters, retains characteristics of the horseshoe prior, and avoids computational difficulties encountered in discrete mixture models. We demonstrate the theoretical properties including concentration towards zero, tail dependence, and posterior behaviors. We conduct a simulation study to evaluate the properties of the proposed prior under different settings. We apply our method to X-ray diffraction images to detect pattern changes and we validate the performance of the proposed approach in relation to competitors. This is a joint work with Dr. Brian Reich and Dr. Montserrat Fuentes. Keywords: spatial shrinkage; sparsity; horseshoe estimator.