  We propose a novel use of a recent new computational tool for Bayesian
inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC
is a way to handle models for which the likelihood function may be intractable
or even unavailable and/or too costly to evaluate; in particular, we consider
the problem of eliminating the nuisance parameters from a complex statistical
model in order to produce a likelihood function depending on the quantity of
interest only. Given a proper prior for the entire vector parameter, we propose
to approximate the integrated likelihood by the ratio of kernel estimators of
the marginal posterior and prior for the quantity of interest. We present
several examples.
