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Pal, Subhadip; Sengupta, Subhajit; Mitra, Riten; Banerjee, Arunava

Conjugate priors and posterior inference for the matrix Langevin distribution on the Stiefel manifold. (English) Zbl 1459.62238

Bayesian Anal. 15, No. 3, 871-908 (2020).
Summary: 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.

Cited in 1 Document

MSC:

62R30 Statistics on manifolds
62H10 Multivariate distribution of statistics
62H11 Directional data; spatial statistics
62F15 Bayesian inference
62P10 Applications of statistics to biology and medical sciences; meta analysis

Keywords:

Bayesian inference; conjugate prior; hypergeometric function of matrix argument; matrix Langevin distribution; Stiefel manifold; vectorcardiography

Software:

movMF; rstiefel; BayesDA
PDF BibTeX XML Cite
\textit{S. Pal} et al., Bayesian Anal. 15, No. 3, 871--908 (2020; Zbl 1459.62238)
Full Text: DOI Euclid

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