An empirical Bayes approach to directional data and efficient computation on the sphere

Abstract

This paper proposes a consistent nonparametric empirical Bayes estimator of the prior density for directional data. The methodology is to use Fourier analysis on S2 to adapt Euclidean techniques to this non-Euclidean environment. General consistency results are obtained. In addition, a discussion of efficient numerical computation of Fourier transforms on S2 is given, and their applications to the methods suggested in this paper are sketched.