Empirical Likelihood-Based Bayesian Methodology for Complex Survey Data Sets

• Activity Number: 26
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Sanjay Chaudhuri*+
• Companies: National University of Singapore
• Keywords: Empirical likelihood ; Complex surveys ; Sample likelihood ; Bayesian Statistics

Abstract

In many applications, it is necessary that the data is collected through a complex design. In such datasets the distribution in the sample differs drastically from the distribution in the population. Moreover, the observations may not be independent. Modelling and analysing such datasets has been major interest in statistics. In frequentist paradigm, parameter estimates are usually obtained by solving Horvitz-Thompson estimate of the population sum of estimating equations obtained from the assumed model. These estimators are not likelihood based and thus cannot be directly used in Bayesian paradigm. In this presentation we discuss an alternative empirical likelihood based Bayesian approach to model and analyse such complex datasets. Our method is based on a "sample likelihood", which together with empirical likelihood provides an easy way to include prior information in such analysis. Furthermore, because of the use of empirical likelihood, the procedure is semiparametric and enjoys many advantages over the traditional parametric likelihood. We, shall illustrate our methodology with real data examples.