Conjugate priors and posterior inference for the matrix langevin distribution on the stiefel manifold

Subhadip Pal, Subhajit Sengupta, Riten Mitra, Arunava Banerjee

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)871-908
Number of pages38
JournalBayesian Analysis
Volume15
Issue number3
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Bayesian inference
  • Conjugate prior
  • Hypergeometric function of matrix argument
  • Matrix langevin distribution
  • Stiefel manifold
  • Vectorcardiography

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Conjugate priors and posterior inference for the matrix langevin distribution on the stiefel manifold'. Together they form a unique fingerprint.

Cite this