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September 2020 Conjugate Priors and Posterior Inference for the Matrix Langevin Distribution on the Stiefel Manifold
Subhadip Pal, Subhajit Sengupta, Riten Mitra, Arunava Banerjee
Bayesian Anal. 15(3): 871-908 (September 2020). DOI: 10.1214/19-BA1176


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.


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Subhadip Pal. Subhajit Sengupta. Riten Mitra. Arunava Banerjee. "Conjugate Priors and Posterior Inference for the Matrix Langevin Distribution on the Stiefel Manifold." Bayesian Anal. 15 (3) 871 - 908, September 2020.


Published: September 2020
First available in Project Euclid: 9 October 2019

MathSciNet: MR4132653
Digital Object Identifier: 10.1214/19-BA1176

Keywords: Bayesian inference , conjugate prior , hypergeometric function of matrix argument , matrix Langevin distribution , Stiefel manifold , vectorcardiography


Vol.15 • No. 3 • September 2020
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