Bayesian structured variable selection in linear regression models

Min Wang, Xiaoqian Sun, Tao Lu

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

In this paper we consider the Bayesian approach to the problem of variable selection in normal linear regression models with related predictors. We adopt a generalized singular g-prior distribution for the unknown model parameters and the beta-prime prior for the scaling factor g, which results in a closed-form expression of the marginal posterior distribution without integral representation. A special prior on the model space is then advocated to reflect and maintain the hierarchical or structural relationships among predictors. It is shown that under some nominal assumptions, the proposed approach is consistent in terms of model selection and prediction. Simulation studies show that our proposed approach has a good performance for structured variable selection in linear regression models. Finally, a real-data example is analyzed for illustrative purposes.

Original languageEnglish
Pages (from-to)205-229
Number of pages25
JournalComputational Statistics
Volume30
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Beta-prime prior
  • Consistency
  • Generalized singular g-prior
  • Gibbs sampler
  • Interactions
  • Posterior probability

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