Original version: March 2010, Revised: February 2011
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, while 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-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 many are interested in sparse solutions, reveal connections with some well-established regularization procedures and show some asymptotic results. The performance of the prior is tested through simulations.
Key Words: Heavy tails; High-dimensional data; Lasso; Maximum a posteriori estimation; Relevance vector machine; Posterior consistency; Robust prior; Shrinkage estimation.
The manuscript is available in PDF format.