On a Bayesian Empirical likelihood-based Method for Non-probability Sampling

Music City Center 

In this article, we discuss a Bayesian Empirical Likelihood (BayesEL) based method for complex survey data leading to applications in non-probability sampling. Bayesian formulation of complex survey data presents several computational, methodological, as well as philosophical problems. Since the observations are sampled with unequal probability, the distributions of the observations in the population and the sample are different. Thus when it comes to constructing the posterior, a practioner has a choice of using one of the above distributions. Associated with this, we also need to consider if the posterior is constructed based on the sample or the whole of the finite population. This question is also related to the method used to incorporate the information in the sampling weights in the procedure. We will show that the BayesEL provides an orderly way to construct a posterior for complex survey data by addressing all the above questions. Some properties of the posterior, e.g. asymptotic validity, objective prior construction, etc will be discussed. Finally, an application to the non-probability sampling problem will be presented.