On intrinsic priors for nonnested models

Model selection problems involving nonnested models are considered. Bayes factor based solution to these problems needs prior distributions for the parameters in the alternative models. When the prior information on these parameters is vague default priors are available but, unfortunately, these priors are usually imporper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Intrinsic priors have been introduced for solving this difficulty. While these priors are well established for nested models, their construction for nonnested models is still an open problem. In this latter setting this paper studies the system of functional equations that defines the intrinsic priors. It is shown that the solutions to these equations are obtained from the solutions to a single homogeneous linear functional equation. The Bayes factors associated with these solutions are analyzed. Some illustrative examples are provided and, in particular, location, scale, and location-scale models are considered.