Flexible Learning on the Sphere Via Adaptive Needlet Shrinkage and Selection

This paper introduces an approach for flexible, robust Bayesian modeling of structure in spherical data sets. Our method is based upon a recent construction called the needlet, which is a particular form of spherical wavelet with many favorable statistical and computational properties. We perform shrinkage and selection of needlet coefficients, focusing on two main alternatives: empirical-Bayes thresholding for selection, and the horseshoe prior for shrinkage. We study the performance of the proposed methodology both on simulated data and on a real data set involving the cosmic microwave background radiation. Horseshoe shrinkage of needlet coefficients is shown to yield the best overall performance against some common benchmarks.