On Empirical Likelihood-Based Methods in ABC

• Activity Number: 639
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Sanjay Chaudhuri*+ and David Nott and Pham Thi Kim Cuc
• Companies: National University of Singapore and National University of Singapore and National University of Singapore
• Keywords: ABC ; Empirical likelihood ; Data dependent estimating equations ; Scaled empirical likelihood

Abstract

Most models in natural, engineering and environmental sciences are complex. For many such models it is essentially impossible to specify a likelihood, which complicates their statistical analysis. Approximate Bayesian computation (ABC) does not require explicit specification of likelihoods and thus provides a way to estimate the parameters in such models. However, usual ABC techniques are computationally expensive and could be quite slow. Faster Empirical likelihood (EL) based methods have been proposed as an alternative by several authors. The proposed EL based methods use estimating equations involving the data and the parameters in the model. Such estimating equations are not readily available. In fact, finding such equations are potentially as difficult as finding the likelihoods themselves. In this article we discuss EL based ABC methods, which use estimating equations depending on the observed and the simulated data from the model. We also propose a general and arguably more useful scaled EL based method when multiple samples could be drawn from the model. We illustrate our methods with examples and application to real data sets.