  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.
