Bayesian semiparametric multiple shrinkage

Richard F. MacLehose, David B. Dunson

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)455-462
Number of pages8
JournalBiometrics
Volume66
Issue number2
DOIs
StatePublished - Jun 2010

Keywords

  • Dirichlet process
  • Hierarchical model
  • Lasso
  • MCMC
  • Mixture model
  • Nonparametric
  • Regularization
  • Shrinkage prior

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