Title: Constrained empirical Bayes priors on regression coefficients,
Abstract: Under model uncertainty, empirical Bayes (EB) procedures can have undesirable
properties such as extreme estimates of inclusion probabilities (Scott &
Berger, 2010) or inconsistency under the null model (Liang et al., 2008). To
avoid these issues, we define empirical Bayes priors with constraints that
ensure that the estimates of the hyperparameters are at least as "vague" as
those of proper default priors. In our examples, we observe that constrained EB
procedures are better behaved than their unconstrained counterparts and that
the Bayesian Information Criterion (BIC) is similar to an intuitively appealing
constrained EB procedure.