Generalized double Pareto shrinkage

Abstract

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models.The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors.While it has a spike at zero like the Laplace density, it also has a Student's t-like tail behavior.Bayesian computation is straightforward via a simple Gibbs sampling algorithm.We investigate the properties of the maximum a posteriori estimator, as sparse estimation plays an important role in many problems, reveal connections with some well-established regularization procedures, and show some asymptotic results.The performance of the prior is tested through simulations and an application.