Statistica Sinica 23 (2013), 119-143
doi:http://dx.doi.org/10.5705/ss.2011.048
GENERALIZED DOUBLE
PARETO SHRINKAGE
Artin Armagan,
David B. Dunson and Jaeyong Lee
SAS
Institute Inc., Duke University and Seoul National University
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 
-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.
Key words and phrases:
Heavy tails, high-dimensional data, LASSO, maximum a posteriori
estimation, relevance vector machine, robust prior, shrinkage
estimation.