On a Class of Shrinkage Priors for Covariance Matrix Estimation

We propose a class of scale mixture of uniform distributions to generate shrinkage priors for the covariance matrix. This new class of priors enjoys a number of advantages over the traditional scale mixture of normal priors, including its simplicity in characterizing the prior density based on its first-order derivative and computationally efficiency based on a Gibbs sampler. We first discuss the theory and computational details of this new approach for the covariance matrix estimation. We then extend the basic model to a new class of multivariate conditional autoregressive models for analyzing multivariate areal data. The proposed spatial model can flexibly characterize both the spatial and the outcome correlation structures at an appealing computational cost. Examples in both synthetic data and real-world data show the utility of this new framework in terms of robust estimation as well as improved predictions.