Model Selection when There is "Minimal" Prior Information

Abstract

A NUMBER OF AUTHORS argue that a Bayesian posterior odds criterion is appropriate for model selection.2 This paper considers how to derive this criterion when there is minimal prior information. We propose minimizing measures of prior information relative to the models in question rather than relative to the parameters of the particular models. In so doing, we obtain an expression for the odds that is invariant to the parameterization of the particular models and overcomes certain well known finite sample limiting problems. We illustrate this procedure using two popular measures of information derived from the well known Shannon [26] measure. By minimizing these measures with the sample size held fixed, we obtain the same model selection criterion that Schwarz [25] derived asymptotically for large sample sizes. This expression has a number of desirable properties and is computationally no more