Hierarchical Bayesian approach to skew normal distribution with random effects
Jun Woo Jo1 · Kil Ho Cho2 · Yongku Kim3
123Department of Statistics, Kyungpook National University
Correspondence to: 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
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 October 4, 2024; Revised October 17, 2024; Accepted October 18, 2024.
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 most statistical studies, sample surveys are more commonly conducted than total population surveys. This paper explores Bayesian hierarchical modeling for estimation in surveys that involve non-sample data. In our study, we analyze two different surveys, where the variables of interest exhibit skewed distributions. To address this, we first apply a matching algorithm to align the two surveys and subsequently develop a Bayesian hierarchical model incorporating a skew-normal distribution with noninformative priors and random effects. Bayesian hierarchical models are extensively used in small area estimation. While the Bayesian hierarchical model is conceptually simple, it is adaptable to complex data structures. Molina, Nandram, and Rao (2014) introduced a Bayesian hierarchical model for continuous, right-skewed data. In their work, skewed variables were estimated through log transformation. Our study builds on this by introducing a skew-normal distribution to better accommodate the skewness in the data. The skew-normal distribution, which encompasses the standard normal distribution but includes an additional parameter to regulate skewness, was first introduced by O’Hagan and Leonard (1976). In this study, we evaluate our model through a simulation study and compare its performance with the model proposed by Nandram.
- Keywords : Grid method, hierarchical Bayes, noninformative priors, skew normal distribution, random effects, small area estimation
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