Dirichlet-Laplace priors for optimal shrinkage.

Published

Journal Article

Penalized regression methods, such as L1 regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimensions. This has motivated continuous shrinkage priors, which can be expressed as global-local scale mixtures of Gaussians, facilitating computation. In contrast to the frequentist literature, little is known about the properties of such priors and the convergence and concentration of the corresponding posterior distribution. In this article, we propose a new class of Dirichlet-Laplace priors, which possess optimal posterior concentration and lead to efficient posterior computation. Finite sample performance of Dirichlet-Laplace priors relative to alternatives is assessed in simulated and real data examples.

Full Text

Duke Authors

Cited Authors

  • Bhattacharya, A; Pati, D; Pillai, NS; Dunson, DB

Published Date

  • December 2015

Published In

Volume / Issue

  • 110 / 512

Start / End Page

  • 1479 - 1490

PubMed ID

  • 27019543

Pubmed Central ID

  • 27019543

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2014.960967

Language

  • eng