Expected-posterior prior distributions for model selection

We consider the problem of comparing parametric models using a Bayesian approach. A new method of developing prior distributions for the model parameters is presented, called the expected‐posterior prior approach. The idea is to define the priors for all models from a common underlying predictive distribution, in such a way that the resulting priors are amenable to modern Markov chain Monte Carlo computational techniques. The approach has subjective Bayesian and default Bayesian implementations, and overcomes the most significant impediment to Bayesian model selection, that of ensuring that prior distributions for the various models are appropriately compatible.