Approximate Bayesian computation for the elimination of nuisance parameters

We propose a novel use of the approximate Bayesian methodology. ABC is a way to handle models for which the likelihood function may be considered intractable; this situation is closely related to the problem of the elimination of nuisance parameters: the model may contain a high-dimensional latent structure, so any elaboration of the likelihood function could be difficult or even impossible when the analysis is focused just on few parameters. We propose to use ABC to approximate the likelihood function of the parameter of interest.