Statistica Sinica 26 (2016), 97-117
Abstract: We propose discrete determinantal point processes (DPPs) for priors on the model parameter in Bayesian variable selection. By our variable selection method, collinear predictors are less likely to be simultaneously selected due to the repulsion property of discrete DPPs. Three types of DPP priors are proposed. Our method is an empirical Bayes approach, so hyperparameters are estimated by maximizing the marginal likelihood. We show the efficiency of the proposed priors through numerical experiments and applications to collinear datasets.
Key words and phrases: Collinearity, empirical Bayes, g-prior.