Approximate integrated likelihood via ABC methods

Clara Grazian (Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Italy; Université Paris-Dauphine, Paris, France; and CREST, Paris, France)

Brunero Liseo (MEMOTEF, Sapienza Università di Roma, Italy)

Abstract

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.

Keywords

Monte Carlo methods, nuisance parameters, profile likelihood, Neyman and Scott problem, quantile estimation, semiparametric regression

2010 Mathematics Subject Classification

Primary 62F15. Secondary 62-04.

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Published 6 March 2015