Mathematics Colloquium Friday, October 19 at 2:00pm in NS 212D

Title: A Bayesian Framework for Modeling Data on the Stiefel Manifold. When/Where: 2:00pm Friday, October 19th, Natural Sciences Building, Room 212D Speaker: Subhadip Pal

Title:                         A Bayesian Framework for Modeling Data on the Stiefel Manifold.

When/Where:           2:00pm Friday, October 19th, Natural Sciences Building, Room 212D

Speaker:                   Subhadip Pal

Department of Bioinformatics and Biostatistics at UofL

Abstract:

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like manifolds. Here, we present a unified Bayesian framework for inference on the Stiefel manifold using the Matrix Langevin distribution. Specifically, we propose a novel family of conjugate priors and establish a number of theoretical properties relevant to statistical inference. 

Conjugacy enables translation of these properties to their corresponding posteriors, which we exploit to develop the posterior inference scheme. For the implementation of the posterior computation, including the posterior sampling, we adopt a novel computational procedure for evaluating the hypergeometric function of matrix arguments that appears as normalization constants in the relevant densities.

Keywords: Bayesian Inference, Conjugate Prior, Hypergeometric Function of Matrix Argument, Matrix Langevin Distribution, Stiefel Manifold, Diffusion Tensor imaging.

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University of Louisville, Department of Mathematics.
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