Heavy-tailed continuous shrinkage priors, such as the horseshoe prior, are widely used for sparse estimation problems. However, there is limited work extending these priors to explicitly incorporate multivariate shrinkage for regressors with grouping structures. Of particular interest in this article, is regression coefficient estimation where pockets of high collinearity in the regressor space are contained within known regressor groupings. To assuage variance inflation due to multicollinearity we propose the gro…