  The Stiefel manifold $V_{p,d}$ is the space of all $d \times p$ orthonormal
matrices, with the $d-1$ hypersphere and the space of all orthogonal matrices
constituting special cases. In modeling data lying on the Stiefel manifold,
parametric distributions such as the matrix Langevin distribution are often
used; however, model misspecification is a concern and it is desirable to have
nonparametric alternatives. Current nonparametric methods are Fr\'echet mean
based. We take a fully generative nonparametric approach, which relies on
mixing parametric kernels such as the matrix Langevin. The proposed kernel
mixtures can approximate a large class of distributions on the Stiefel
manifold, and we develop theory showing posterior consistency. While there
exists work developing general posterior consistency results, extending these
results to this particular manifold requires substantial new theory. Posterior
inference is illustrated on a real-world dataset of near-Earth objects.
