Bayesian Covariance Estimation for Multi-group Matrix-variate Data
Year: 2024
Type: article
Abstract: Multi-group covariance estimation for matrix-variate data with small within-group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation methods which shrink an unstructured, group-specific covariance either across groups towards a pooled covariance or within each group towards a Kronecker structure have been developed. However, in many applications, it is unclear which approach will result in more accurate covariance estimates. In this article, we present a hierarchical prior distribution which flexibly allows for both types of shrinkage. The prior linearly combines shrinkage across groups towards a shared pooled covariance and shrinkage within groups towards a group-specific Kronecker covariance. We illustrate the utility of the proposed prior in speech recognition and an analysis of chemical exposure data.
Source: Bayesian Analysis
DOI: 10.1214/24-ba1449
Authors: Elizabeth Bersson, Peter D. Hoff
Institution: Duke University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4400278764