Bayesian Estimation of Intensity Surfaces on the Sphere via Needlet Shrinkage and Selection

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Date

2011

Authors

Scott, James G.

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Abstract

This paper describes an approach for Bayesian modeling in spherical datasets. 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, and Bayesian local shrinkage rules. We study the performance of the proposed methodology 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.

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Citation

Scott, James G. "Bayesian estimation of intensity surfaces on the sphere via needlet shrinkage and selection." Bayesian Analysis, Vol. 6, No. 2 (2011): 307-327.