title: Bayesian Model Selection in High-Dimensional Settings.
abstract: Standard assumptions incorporated into Bayesian model selection procedures result in procedures that are not competitive with commonly used penalized likelihood methods. We propose modifications of these methods by imposing nonlocal prior densities on model parameters. We show that the resulting model selection procedures are consistent in linear model settings when the number of possible covariatespis bounded by the number of observationsn, a property that has not been extended to other model selection procedures. In addition to consistently identifying the true model, the proposed procedures provide accurate estimates of the posterior probability that each identified model is correct. Through simulation studies, we demonstrate that these model selection procedures perform as well or better than commonly used penalized likelihood methods in a range of simulation settings. Proofs of the primary theorems are provided in the Supplementary Material that is available online.
authors.affiliation: Ad interim Division Head of Quantitative Sciences and Professor of Biostatistics at M.D. Anderson Cancer Center, Houston, TX 77030.
authors.forename: Valen E
authors.initials: VE
authors.lastname: Johnson
authors.affiliation: Director of the Biostatistics & Bioinformatics Unit, Institute for Research in Biomedicine of Barcelona, Barcelona, Spain.
authors.forename: David
authors.initials: D
authors.lastname: Rossell
keywords: Adaptive LASSO; Dantzig selector; Elastic net; Intrinsic Bayes factor; Intrinsic prior; Nonlocal prior; Nonnegative garrote; Oracle; g-prior