Model Complexity and Model Priors

Abstract

In hierarchical models it is often hard to specify a (hyper-)prior distribution for a model parameter at the highest level of the model. Several authors suggested to de¯ne a hyperprior as some decreasing function of "model complexity" or "generalized degees of freedom". In this paper the proposal is discussed froma conceptual point of view. In particular, "model complexity" is evaluated as amodel discriminating transformation of the hyperparameter. Also, criteria for model choice of the form "goodness of ¯t - penalty" are related to non-informative (reference) priors for model parameters in representative examples.