Bayesian High-Dimensional Grouped-Regression Using Sparse Projection-posterior

We present a novel Bayesian approach for high-dimensional grouped regression under sparsity.We leverage a sparse projection method that uses a sparsity-inducing map to induce a posterior on a lower-dimensional parameter space.Our method introduces three distinct projection maps based on popular penalty functions: the Group LASSO projection-posterior, the Group SCAD projection-posterior, and the Adaptive Group LASSO projection-posterior.Each projection map is constructed to immerse posterior samp