EMPIRICAL LIKELIHOOD, CLASSIFICATION AND APPROXIMATE BAYESIAN COMPUTATION

Abstract

Many models used in real life often have complex likelihood and many cases have intractable likelihood. Statistically inference on those models has been studied by many authors in recent time. One set of such method falls under the category of approximate Bayesian computation (ABC). In this thesis we discuss new procedures in that category. We first consider approximating ABC-Markov chain Monte Carlo (MCMC) using flexible classifiers where the likelihood ratio in the acceptance probability is replaced by the odds in Bayes classification. The odds are estimated using random forests classifiers. We propose empirical likelihood (EL) based methods where the constraints are function of the observation not dependent on the parameters. Our approach differs from the traditional EL approaches where estimating parameter based estimating equations are required. We also consider a generalized regression adjustment method to improve the efficiency of estimating the posterior in an ABC setting.