Predictive probability as a criterion for model selection

A model selection criterion based on Bayesian predictive densities is derived. Starting with an improper prior distribution of the model parameters and using one portion of the data, a proper distribution is obtained which is further used as a prior for obtaining predictive densities according to the model and the first portion of the data. The remaining portion is used to validate the model through the obtained predictive densities. The procedure is applied to the set of linear regression models. The performance of the criterion is illustrated by simulation results.