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Abstract:
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In regression problems where the unknown coefficients may have some known structure while also be sparse, there are few options for prior distributions that encourage can encourage simultaneously structured and sparse estimates. Of those that exist, most are limited in the amount of structure they can accommodate. In this paper we further generalize the structured shrinkage priors that generalize multivariate normal, Laplace, exponential power and normal-gamma priors in Griffin and Hoff (2019) by introducing correlated priors for scale distributions. The introduction of correlated priors for scale distributions allows us to explore the extent of possibly fundamental tensions between structure and shrinkage. We address the computational challenges that arise when using these prior distributions, and demonstrate how a flexible elliptical slice sampling procedure, and demonstrate that these priors can be used to introduce structure while preserving sparsity of the corresponding penalized estimate given by the posterior mode.
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