Model selection using mass-nonlocal prior

Abstract

Bayesian variable selection is an active research area. The paper proposes a variable selection technique by taking advantages of two distinctive approaches of Bayesian variable selection, namely spike and slab prior and nonlocal prior. Contrary to the local priors, nonlocal priors put zero mass at null values of the parameters. The proposed method uses posterior median as the parameter estimates and asymptotic consistency is established. The Bayesian implementation is proposed via Gibbs sampling. The full conditional distributions are provided. Extensive numerical study indicates superiority of the proposed procedure compared to its competitors. Most importantly, the procedure works well in low signal situation which is not the case in general.