Power-Conditional-Expected Priors: Using g-Priors With Random Imaginary Data for Variable Selection. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Fouskakis, Dimitris; Ntzoufras, Ioannis
• Is Part Of: Journal of computational and graphical statistics. Volume 25:Issue 3(2016)
• Page Start: 647
• Page End: 664
• Publication Date: 2016-07-02
• Subjects: Bayes factors -- Conjugate prior -- Objective model selection methods -- Power-prior -- Training sample -- Unit-information prior; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2015.1036996
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract : The Zellner's g -prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior setups can be expressed as power-priors with fixed set of imaginary data. In this article, we borrow ideas from the power-expected-posterior (PEP) priors to introduce, under the g -prior approach, an extra hierarchical level that accounts for the imaginary data uncertainty. For normal regression variable selection problems, the resulting power-conditional-expected-posterior (PCEP) prior is a conjugate normal-inverse gamma prior that provides a consistent variable selection procedure and gives support to more parsimonious models than the ones supported using the g -prior and the hyper- g prior for finite samples. Detailed illustrations and comparisons of the variable selection procedures using the proposed method, the g -prior, and the hyper- g prior are provided using both simulated and real data examples. Supplementary materials for this article are available online.