Nearly optimal Bayesian shrinkage for high-dimensional regression

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes posterior consistency for linear regression with a class priors, which has heavy and flat tail allocates sufficiently large probability mass very small neighborhood zero. While enjoying its efficiency simulations, prior can lead to nearly optimal contraction rate variable selection as spike-and-slab prior. Our numerical results show that under consistency, methods yield better than regularization such LASSO SCAD. also BvM-type result, leads convenient way uncertainty quantification coefficient estimates.