Casella et al. [2, (2009)] proved that, under very general conditions, for normal linear models the Bayes factor for a wIDe class of prior distributions, including the intrinsic priors, is consistent when the number of parameters does not grow with the sample size n. The special attention paID to the intrinsic priors is due to the fact that they are nonsubjective priors, and thus accessible priors for complex models.
The case where the number of parameters of nested models grows as O(n α ) for α ≤ 1 was consIDered in Moreno et al. [13, (2010)], in which it was proved that the Bayes factor for intrinsic priors is consistent for the case where both models are of order O(n α ) for α < 1, and for α = 1 is consistent except for a small set of alternative models. The small set of models for which consistency does not hold was characterized in terms of a pseudo-distance between models.
The goal of the present article is to extend the above results to the case where the linear models are nonnested. As the comparison of nonnested models calls for a method of encompassing, for proving consistency we use encompassing from below in this paper.