On Bayesian Empirical Likelihood-based Method for Complex Survey Data with Application to Non-probability Sampling

Authors

Md Hasibur Rahman, University of Nebraska-LincolnFollow

First Advisor

Sanjay Chaudhuri

Committee Members

Souparno Ghosh, Indranil Mukhopadhyay

Date of this Version

12-2025

Document Type

Thesis

Citation

A thesis presented to the faculty of the Graduate College at the University of Nebraska in partial fulfilment of requirements for the degree of Master of Science

Major: Statistics

Under the supervision of Professor Sanjay Chaudhuri

Lincoln, Nebraska, December 2025

Comments

Copyright 2025, Md Hasibur Rahman. Used by permission

Abstract

This thesis develops a Bayesian empirical likelihood (BEL) framework for inference under complex survey designs and extends it to non-probability sampling. Parametric likelihood based methods are difficult to apply to complex survey data because the likelihood is rarely available in closed form. EL provides a flexible alternative by replacing the parametric likelihood with an empirical likelihood constructed from moment conditions. The proposed method first integrates empirical likelihood constraints with survey design features then extends BEL to non-probability sampling through selection models and design consistent restrictions. Posterior inference is carried out using a Metropolis–Hastings MCMC algorithm. A real-data analysis further illustrates the framework’s ability to correct selection bias when combining probability and non-probability samples.

Advisor: Sanjay Chaudhuri