Robust Bayesian variable selection in linear models with spherically symmetric errors

Yuzo Maruyama, William E. Strawderman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper studies Bayesian variable selection in linear models with general spherically symmetric error distributions.We construct the posterior odds based on a separable prior, which arises as a class ofmixtures of Gaussian densities. The posterior odds for comparing among nonnull models are shown to be independent of the error distribution, if this is spherically symmetric. Because of this invariance, we refer to our method as a robust Bayesian variable selection method.We demonstrate that our posterior odds have model selection consistency, and that our class of prior functions are the only ones within a large class which are robust in our sense.

Original languageEnglish (US)
Pages (from-to)992-998
Number of pages7
JournalBiometrika
Volume101
Issue number4
DOIs
StatePublished - Dec 1 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Bayesian variable selection
  • Fully Bayes method
  • Model selection consistency
  • Posterior odds

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