This paper considers parametric statistical decision problems
conducted within a Bayesian nonparametric context. Our work was
motivated by the realisation that typical parametric model selection
procedures are essentially incoherent. We argue that one solution to
this problem is to use a flexible enough model in the first place, a
model that will not be checked no matter what data arrive. Ideally,
one would use a nonparametric model to describe all the uncertainty
about the density function generating the data. However, parametric
models are the preferred choice for many statisticians, despite the
incoherence involved in model checking, incoherence that is quite
often ignored for pragmatic reasons. In this paper we show how
coherent parametric inference can be carried out via decision theory
and Bayesian nonparametrics. None of the ingredients discussed here
are new, but our main point only becomes evident when one sees all
priors-even parametric ones-as measures on sets of densities as
opposed to measures on finite-dimensional parameter spaces.