Bayesian One-Sided Variable Selection

This paper presents a novel Bayesian variable selection approach that accounts for the sign of the regression coefficients based on multivariate one-sided tests. We propose a truncated g prior to specify a prior distribution of coefficients with anticipated signs in a given model. Informative priors for the direction of the effects can be incorporated into prior model probabilities. The best subset of variables is selected by comparing the posterior probabilities of the possible models. The new Bayesian one-sided variable selection procedure has higher chance to include relevant variables and therefore select the best model, if the anticipated direction is accurate. For a large number of candidate variables, we present an adaptation of a Bayesian model search method for the one-sided variable selection problem to ensure fast computation. In addition, a fully Bayesian approach is used to adjust the prior inclusion probability of each one-sided model to correct for multiplicity. The performance of the proposed method is investigated using several simulation studies and two real data examples.