Power-Conditional-Expected Priors: Using g -Priors With Random Imaginary Data for Variable Selection

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.