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Abstract:
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Probability distributions on the Stiefel or Grassmann manifolds and their special cases have primarily been used as statistical models for data that are naturally understood as directions, axes, or rotations; however, these distributions are increasingly finding application as components of complex probability models, for example in latent factor models and models for matrices based on eigendecompositions. In such applications, it is often desirable to introduce dependence between special manifold elements in order to share information across related groups or neighboring observations, but the literature on multivariate distributions for special manifold elements is limited to special cases. Here we introduce multivariate distributions for elements of the Stiefel and Grassmannian manifolds which are constructed from metrics on those spaces and have a number of appealing properties, including a graphical model interpretation. We provide a variety of illustrative examples and two data applications.
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