Hamiltonian Monte Carlo sampling in Bayesian empirical likelihood computation
Following Owen (1988), there has developed a vast literature on the empirical likelihood (EL) based estimation and inference methods that allow for parametric restrictions by specifying a set of unbiased estimating equations without making any explicit assumptions about the form of the underlying distribution function of the data. In recent years, beginning with Lazar (2003), several researchers have adapted the EL analysis in Bayesian paradigm. However, Bayesian EL functions give rise to complex posterior distributions, often with non-convex boundaries and no known analytic formula. In this talk, I will discuss an efficient Hamiltonian Monte Carlo method for sampling from such EL based posterior distributions. The method will use hitherto unknown properties of the gradient of the underlying log EL function. I will provide illustrative examples and an application from small area estimation. This is a joint work with Sanjay Chaudhuri and Teng Yin at the National University of Singapore.