Hierarchical Bayesian modeling with skew normal distribution†
Jun Woo Jo1 · Kil Ho Cho2 · Yongku Kim3
123Department of Statistics, Kyungpook National University
Correspondence to: † This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(RS-2023-00240494).
1 Graduate student, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
2 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
3 Corresponding author: Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail: kim.1252@knu.ac.kr
1 Graduate student, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
2 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
3 Corresponding author: Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail: kim.1252@knu.ac.kr
Received November 13, 2023; Revised December 4, 2023; Accepted December 5, 2023.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- In fact, most statistical surveys consist of sample surveys, not total surveys. This paper considers the Bayesian hierarchical modeling for estimation in surveys with non-sample. In our study, there are two different surveys and the variables of interest consist of skewed values. For this problem, we first use a matching algorithm for two surveys and then develop a Bayesian hierarchical model with skew normal distribution and noninformative priors. Bayesian hierarchical models have been widely used for small area estimation. The Bayesian hierarchical model is based on a very simple model, and can be set up using a very complex data model. The paper by Molina, Nandram, and Rao (2014) introduces a Bayesian hierarchical model of continuous, right-skewed data. In this study, skewed variables were estimated using log transformation, and our purpose is to develop the previous method using skew normal distribution for model assumptions. Skew normal distribution, a family of distributions including the standard normal but with an extra parameter to regulate skewness was first introduced by O’Hagan and Leonard(1976). Our model was evaluated by comparing with Nandram’s model in simulation study.
- Keywords : Grid method, hierarchical Bayes, noninformative priors, skew normal distribution, survey.
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