On MCMC Procedure for Bayesian Empirical Likelihood

• Activity Number: 433
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Sanjay Chaudhuri*+ and Teng Yin
• Companies: National Univ. of Singapore and
• Keywords: Bayesian empirical likelihood ; empty set problem ; MCMC ; RJMCMC

Abstract

In Bayesian Empirical Likelihood procedure one replaces the usual parametric likelihood of the data with a non-parametric empirical likelihood estimated from available estimating equation based constraints. Since no analytic form of the posterior is available, MCMC procedure is used. However, the use of empirical likelihood implies that the support of the posterior depends on the data. This support is extremely difficult to determine for even simple multiple regression problems. Such "empty-sets" make MCMC slow. In this talk we discuss a way to make proposals in MCMC procedure to avoid this empty set problem in many problems. Using our method it is possible to avoid parallel tempering which is a requirement in many Bayesian empirical likelihood methods. Our method also extends to RJMCMC. We shall discuss simulated examples and application to real data sets. This work is joint with Yin Teng, Department of Statistics and Applied Probability, National University of Singapore.