Bayesian analysis of matrix data with rstiefel

TL;DR

This paper demonstrates the application of the R-package "rstiefel" for Bayesian analysis of matrix-variate data, focusing on reduced-rank mean estimation and social network modeling, utilizing specialized distributions on the Stiefel manifold.

Contribution

It introduces practical Bayesian methods for matrix data analysis using the "rstiefel" package, with examples in mean estimation and social network modeling.

Findings

Successful Bayesian estimation of reduced-rank mean matrices.

Modeling of social networks using matrix-variate distributions.

Implementation of sampling from matrix-variate von Mises-Fisher and Bingham distributions.

Abstract

We illustrate the use of the R-package "rstiefel" for matrix-variate data analysis in the context of two examples. The first example considers estimation of a reduced-rank mean matrix in the presence of normally distributed noise. The second example considers the modeling of a social network of friendships among teenagers. Bayesian estimation for these models requires the ability to simulate from the matrix-variate von Mises-Fisher distributions and the matrix-variate Bingham distributions on the Stiefel manifold.