search for


A Bayesian approach with propensity scores for prediction of unknown responses
Journal of the Korean Data & Information Science Society 2021;32:1353-62
Published online November 30, 2021;
© 2021 Korean Data and Information Science Society.

Juhee Lee1 · Eun Jin Jang2 · Dal Ho Kim3

13Department of Statistics, Kyungpook National University
2Department of Information Statistics, Andong National University
Correspondence to: 1 Doctor program, Department of Statistics, Kyungpook National University, Daegu 41566, Korea.
2 Associate professor, Department of Information Statistics, Andong National University, Andong 36729, Korea.
3 Corresponding author: Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail:
Received October 25, 2021; Revised November 2, 2021; Accepted November 4, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
A non-probability sample is a sample in which the probability of selection is unknown, and not all individual in the population has a chance of being selected. Since non-probability sampling does not require a survey frame, it is a fast, inexpensive, and comfortable way of obtaining data. However, using the non-probability samples can be risky because they may obtain several kinds of biases, such as frame coverage bias, selection bias, and non-response. In order to solve these problems, we suggest the method for the prediction of unknown responses. We apply the Bayesian hierarchical model for analyzing the probability of selection and use the Metropolis-Hastings sampler and Laplace approximation. We predict the response of non-sampled groups using Bayesian bootstrap in simulation data and the bone mineral density data in NHANES III.
Keywords : Bayesian hierarchical model, non-probability sampling, probit model, propensity score.