Local robustness of Bayes factors for nonparametric alternatives
Cinzia Carota · Lecture notes-monograph series · 1996
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.Fo known up to a real parameter 0, into a mixture of Dirichlet processes.More precisely, conditionally on 0, FQ 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 Fo 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.