文章基本信息

标题：Conjugate Priors and Posterior Inference for the Matrix Langevin Distribution on the Stiefel Manifold
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作者：Subhadip Pal ; Subhajit Sengupta ; Riten Mitra 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2020
卷号：15
期号：3
页码：871-908
DOI：10.1214/19-BA1176
语种：English
出版社：International Society for Bayesian Analysis
摘要：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.
关键词：Bayesian inference; conjugate prior; hypergeometric function of matrix argument; matrix Langevin distribution; Stiefel manifold; vectorcardiography