Statistics and Its Interface
Volume 8 (2015)
Special Issue on Modern Bayesian Statistics (Part II)
Guest Editor: Ming-Hui Chen (University of Connecticut)
Approximate integrated likelihood via ABC methods
Pages: 161 – 171
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.
Monte Carlo methods, nuisance parameters, profile likelihood, Neyman and Scott problem, quantile estimation, semiparametric regression
2010 Mathematics Subject Classification
Primary 62F15. Secondary 62-04.