Bayesian comparison of models with inequality and equality constraints

A Bayesian model selection procedure for comparing models subject to inequality and/or equality constraints is proposed. An encompassing prior approach is used, and a general form of the Bayes factor of a constrained model against the encompassing model is derived. A simple estimation method is proposed which can estimate the Bayes factors for all candidate models simultaneously by using one set of samples from the encompassing model. A simulation study and a real data analysis demonstrate performance of the method.