1. Prior distributions for structured semi-orthogonal matrices
- Author
-
Jauch, Michael, Düker, Marie-Christine, and Hoff, Peter
- Subjects
Statistics - Methodology ,Mathematics - Statistics Theory - Abstract
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or smoothness. From a Bayesian perspective, these structural assumptions should be incorporated into an analysis through the prior distribution. In this work, we introduce a general approach to constructing prior distributions for structured semi-orthogonal matrices that leads to tractable posterior inference via parameter-expanded Markov chain Monte Carlo. We draw upon recent results from random matrix theory to establish a theoretical basis for the proposed approach. We then introduce specific prior distributions for incorporating sparsity or smoothness and illustrate their use through applications to biological and oceanographic data., Comment: 31 pages, 5 figures
- Published
- 2025