On Bayes factors for nonparametric alternatives

In this paper we derive global Bayes factors for the comparison of a parametric model with a nonparametric alternative. The alternative is constructed by embedding the parametric model in a mixture of Dirichlet processes. Results include a general explicit form for partially exchangeable sequences as well as closed form expressions in the context one-way analysis of variance.Our results raises concerns on how how to define and use Bayes factors for nonparametric alternatives. In particular, an important and disturbing corollary of our assumption is that, when no duplicate observations occur, the Bayes factor depends on the data only through the sample size.