Local robustness of Bayes factors for nonparametric alternatives

In this paper we consider a particular Bayes factor B for comparing a fixed parametric model against a nonparametric alternative, and we investigate its local sensitivity to the sampling distribution. The nonparametric alternative is constructed by embedding the parametric model, characterized by a d.f. F-o known up to a real parameter theta, into a mixture of Dirichlet processes. More precisely, conditionally on theta, F-o represents the mean of a random d.f. which is assumed to be a Dirichlet Process. So, for the Bayes factor B, sensitivity to perturbations of the sampling distribution F-o and sensitivity to small departures from the fixed Dirichlet process parameter are the same problem. Here we consider B as a (non ratio-linear) functional defined on a set of sampling d.f.'s and maximize its first von Mises derivative over this set. In particular, mixture and density bounded sets are considered.