Bayesian variable selection with shrinking and diffusing priors

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in the sense that the posterior probability of the true model converges to one even when the number of covariates grows nearly exponentially with the sample size. This is arguably the strongest selection consistency result that has been available in the Bayesian variable selection literature; yet the proposed method can be carried out through posterior sampling with a simple Gibbs sampler. Furthermore, we argue that the proposed method is asymptotically similar to model selection with the L0 penalty. We also demonstrate through empirical work the fine performance of the proposed approach relative to some state of the art alternatives.

Original languageEnglish (US)
Pages (from-to)789-817
Number of pages29
JournalAnnals of Statistics
Volume42
Issue number2
DOIs
StatePublished - Apr 2014
Externally publishedYes

Keywords

  • Bayes factor
  • Hierarchical model
  • High dimensional data
  • Shrinkage
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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