Structured Shrinkage Priors

In many regression settings the unknown coefficients may have some known structure, for instance they be ordered in space or correspond to a vectorized matrix tensor. At same time, sparse, with nearly exactly equal zero. However, commonly used priors and corresponding penalties do not encourage simultaneously structured sparse estimates. this paper we develop shrinkage that generalize multivariate normal, Laplace, exponential power normal-gamma priors. These allow correlated priori without sacrificing elementwise sparsity shrinkage. The primary challenges working these are computational, as intractable integrals full conditional distributions needed approximate posterior mode simulate from distribution non-standard. We overcome issues using flexible elliptical slice sampling procedure, demonstrate can introduce structure while preserving sparsity.