We consider likelihood and Bayes analyses for the symmetric matrix von Mises-Fisher (matrix Fisher) distribution, which is a common model for three-dimensional orientations (represented by 3x3 orthogonal matrices with a positive determinant). One important characteristic of this model is a 3x3...

A variety of existing symmetric parametric models for 3-D rotations found in both statistical and materials science literatures are considered from the point of view of the “uniform-axis-random-spin” (UARS) construction. One-sample Bayes methods for non-informative priors are provided for...