Objective Bayesian Variable Selection

Abstract

A novel fully automatic Bayesian procedure for variable selection in normal regression models is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors for model selection problems; that is, they are derived from the model structure and are free from tuning parameters. Thus they can be seen as objective priors for variable selection. The stochastic search is based on a Metropolis–Hastings algorithm with a stationary distribution proportional to the model posterior probabilities. The procedure is illustrated on both simulated and real examples.