A New Criterion for Variable Selection

The variable/model selection problem is reexamined from a Bayesian perspective using data splitting to establish a joint prior for the relevent parameters. This allows for the required integrations that have to be performed to be over the same dimensional parameter space. It also produces a result which is independent of the scaling of both the independent as well as dependent variables. The posterior probability of each model M∞ is calculated, where the subscript α is used to index the subsets of the predictor variables. This probability is shown to be asymptotically equal to 1, if Mα is the correct model. A new model selection criterion is also derived from this expression. Examples using simulated data and real data sets are provided.