We develop a nonparametric Bayes factor for testing the fit of a
parametric model. We begin with a nominal parametric family which we then embed
into an infinite-dimensional exponential family. The new model then has a
parametric and nonparametric component. We give the log density of the
nonparametric component a Gaussian process prior. An asymptotic consistency
requirement puts a restriction on the form of the prior, leaving us with a
single hyperparameter for which we suggest a default value based on simulation
experience. Then we construct a Bayes factor to test the nominal model versus
the semiparametric alternative. Finally, we show that the Bayes factor is
consistent. The proof of the consistency is based on approximating the model by
a sequence of exponential families.