Variational Bayes for Fast and Accurate Empirical Likelihood Inference

Abstract

We develop a fast and accurate approach to approximate posterior distributions in the Bayesian empirical likelihood framework. Bayesian empirical likelihood allows for the use of Bayesian shrinkage without specification of a full likelihood but is notorious for leading to several computational difficulties. By coupling the stochastic variational Bayes procedure with an adjusted empirical likelihood framework, the proposed method overcomes the intractability of both the exact posterior and the arising evidence lower bound objective, and the mismatch between the exact posterior support and the variational posterior support. The optimization algorithm achieves fast algorithmic convergence by us..