A Bayesian Empirical Likelihood Approach to Complex Survey and Non-Probability Data

Thomas M. Menino Convention & Exhibition Center 

This paper proposes a Bayesian empirical likelihood (BEL) framework for analyzing complex survey data and extends it to non-probability sampling. Standard parametric likelihood methods are often hard to use with complex survey designs because the likelihood is rarely available in closed form. Empirical likelihood offers a flexible alternative by replacing the parametric likelihood with likelihoods based on moment conditions.
The proposed approach incorporates survey design features directly into the empirical likelihood framework. It is then extended to non-probability samples using selection models and design-consistent constraints. Posterior inference is conducted using a Metropolis–Hastings MCMC algorithm. A real-data application demonstrates that the proposed method can reduce selection bias when combining probability and non-probability samples.

Bayesian empirical likelihood

Complex survey designs

non-probability sampling

MCMC algorithm

Metropolis–Hastings MCMC 

Section on Bayesian Statistical Science