Abstract (EN)

Recent developments allow Bayesian analysis also when the likelihood function L(θ;y) is intractable, that means it is analytically unavailable or computationally prohibitive to evaluate. These methods are known as ``approximate Bayesian computation" (ABC) or likelihood-free methods and are characterized by the fact that the approximation of the posterior distribution is obtained without explicitly evaluating the likelihood function. This kind of analysis is popular in genetic and financial settings. The likelihood may be unavailable because of a high-dimensional latent structure and this situation is closely related to the problem of eliminating nuisance parameters. We propose a novel use of the ABC methodology. 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 distributions for the quantity of interest. We present several examples, both parametric and semiparametric.