This paper proposes a consistent nonparametric empirical Bayes estimator of the prior density for directional data. The methodology is to use Fourier analysis on $S^2$ 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 $S^2$ is given, and their applications to the methods suggested in this paper are sketched.
"An empirical Bayes approach to directional data and efficient computation on the sphere." Ann. Statist. 24 (1) 232 - 254, February 1996. https://doi.org/10.1214/aos/1033066208