On a Class of Shrinkage Priors for Covariance Matrix Estimation

TL;DR

This paper introduces a new class of shrinkage priors for covariance matrix estimation using scale mixtures of uniform distributions, offering simplicity, flexibility, and efficient computation, especially in high-dimensional and spatial data contexts.

Contribution

It develops a novel, flexible prior class with an easy Gibbs sampler, extending to multivariate spatial models for improved covariance estimation and prediction.

Findings

Demonstrates robust covariance estimation with synthetic and real data.

Shows improved predictive performance over traditional methods.

Provides an efficient Gibbs sampler for high-dimensional problems.

Abstract

We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture of normal priors, including its simplicity and flexibility in characterizing the prior density. We also exhibit a simple, easy to implement Gibbs sampler for posterior simulation which leads to efficient estimation in high dimensional problems. We first discuss the theory and computational details of this new approach and then extend the basic model to a new class of multivariate conditional autoregressive models for analyzing multivariate areal data. The proposed spatial model flexibly characterizes both the spatial and the outcome correlation structures at an appealing computational cost. Examples consisting of both synthetic and real-world data show the utility of this new framework in terms of robust estimation as well as improved predictive performance.