Bayesian Analysis of Matrix-Langevin on the Stiefel Manifold

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Subhajit Sengupta* and Subhadip Pal and Arunava Banerjee and Yuan Ji
• Companies: Northshore University HealthSystem and University of Florida and University of Florida and The University of Chicago
• Keywords: Matrix-Langevin ; Non-parametric Bayesian ; Stiefel

Abstract

Analysis of directional data comprises one of the major sub-fields of study in Statistics. Directional statistics deals with observations that are unit vectors, or sets or ordered tuples of unit vectors, in the n-dimensional space R^n. Since the sample space is not the usual Euclidean space, standard methods developed for the statistical analysis of univariate or multivariate data do not apply immediately. Stated differently, incorporating the intrinsic structure of the sample space is essential to the proper analysis of such data. Parametric as well as non-parametric Bayesian analysis of the Matrix-Langevin distribution on the Stiefel manifold are presented here. An associated hybrid Gibbs sampler with adaptive rejection sampling is also developed. Inference on simulated data is presented to demonstrate the efficacy of the framework. The parametric Bayesian analysis presented here is more general than what was presented earlier. Standard extensions to finite mixture of Matrix-Langevin, Dirichlet Process (DP) Mixture of Matrix-Langevin, as well as variational inference for the DP Mixture model are also discussed.