ABSTRACT
In a very interesting and basic paper, [3] argue that it makes sense to talk of an optimal objective prior in model selection. They make this plausible by providing a set of definitive properties for such a prior and then producing a prior which indeed has all these properties. Just to give a flavor of these properties, we give a few of our favourites. These are the more usual sense of the posterior increasingly putting most of its mass on the true model, i.e. Model Selection Consistency (Criterion 2), Information Consistency (Criterion
in Bayesian
Criteria (Criterion 5), and Invariance under certain groups of transformations (Criterion 7).
