  Orthonormal matrices play an important role in reduced-rank matrix
approximations and the analysis of matrix-valued data. A matrix Bingham-von
Mises-Fisher distribution is a probability distribution on the set of
orthonormal matrices that includes linear and quadratic terms, and arises as a
posterior distribution in latent factor models for multivariate and relational
data. This article describes rejection and Gibbs sampling algorithms for
sampling from this family of distributions, and illustrates their use in the
analysis of a protein-protein interaction network.
