Posterior Odds with a Generalized Hyper-g-Prior

Abstract

Averaged orthogonal rotations of Zellner's g-prior yield general, interpretable, closed form Bayes factors for the normal linear model variable selection problem. Coupled with a model space prior that balances the weight between the identifiable and the unidentifiable models, limiting forms for the posterior odds ratios are seen to yield new expressions for high dimensional model choice.

Keywords:

• Bayes factor
• Indentifiability
• Model selection
• Model space priors
• Singular value decomposition
• Variable selection

2010 Mathematics Subject Classification:

• Primary: 62F07
• 62F15
• Secondary: 62C10

ACKNOWLEDGMENTS

We are very grateful to the editors and referees for their generous suggestions which helped us improve this article.