This paper describes an approach for Bayesian modeling 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
coecients, focusing on two main alternatives: empirical-Bayes thresholding, and
Bayesian local shrinkage rules. We study the performance of the proposed method-
ology both on simulated data and on two real data sets: one involving the cosmic
microwave background radiation, and one involving the reconstruction of a global
news intensity surface inferred from published Reuters articles in August, 1996.
The fully Bayesian approach based on robust, sparse shrinkage priors seems to
outperform other alternatives.