gBF: A Fully Bayes Factor with a Generalized g-prior

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 characteristics of potential interest.