For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner’s g-prior which allows for p > n. A special case of the prior formulation is seen to yield tractable closed forms for marginal densities and Bayes factors which reveal new model evaluation characteristics of potential interest.
"Fully Bayes factors with a generalized g-prior." Ann. Statist. 39 (5) 2740 - 2765, October 2011. https://doi.org/10.1214/11-AOS917