Bayesian semiparametric multiple shrinkage.

Published

Journal Article

High-dimensional and highly correlated data leading to non- or weakly identified effects are commonplace. Maximum likelihood will typically fail in such situations and a variety of shrinkage methods have been proposed. Standard techniques, such as ridge regression or the lasso, shrink estimates toward zero, with some approaches allowing coefficients to be selected out of the model by achieving a value of zero. When substantive information is available, estimates can be shrunk to nonnull values; however, such information may not be available. We propose a Bayesian semiparametric approach that allows shrinkage to multiple locations. Coefficients are given a mixture of heavy-tailed double exponential priors, with location and scale parameters assigned Dirichlet process hyperpriors to allow groups of coefficients to be shrunk toward the same, possibly nonzero, mean. Our approach favors sparse, but flexible, structure by shrinking toward a small number of random locations. The methods are illustrated using a study of genetic polymorphisms and Parkinson's disease.

Full Text

Duke Authors

Cited Authors

  • Maclehose, RF; Dunson, DB

Published Date

  • June 2010

Published In

Volume / Issue

  • 66 / 2

Start / End Page

  • 455 - 462

PubMed ID

  • 19508244

Pubmed Central ID

  • 19508244

Electronic International Standard Serial Number (EISSN)

  • 1541-0420

International Standard Serial Number (ISSN)

  • 0006-341X

Digital Object Identifier (DOI)

  • 10.1111/j.1541-0420.2009.01275.x

Language

  • eng