  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.
