Clara Grazian (Università di Roma “La Sapienza” and Université Paris-Dauphine): Approximate Bayesian computation for the elimination of nuisance parameters

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. We propose a novel use of the approximate Bayesian methodology; an intractable likelihood is related to the problem of the elimination of nuisance parameters. We propose to use ABC to approximate the likelihood function of the parameter of interest. We will present several application of the methodology.

Joint work with Brunero Liseo