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Nonparametric Bayesian copula modeling for shrinkage through the transformation
Journal of the Korean Data & Information Science Society 2023;34:685-95
Published online July 31, 2023;
© 2023 Korean Data and Information Science Society.

Sangwan Kim1 · Jung In Seo2 · Yongku Kim3

13Department of Statistics, Kyungpook National University
2Department of Information Statistics, Andong National University
Correspondence to: This study was carried out with the support of ‘R&D Program for Forest Science Technology (Project No. 2019149B10-2323-0301)’ provided by Korea Forest Service(Korea Forestry Promotion Institute).
1 Graduate Student, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
2 Assistant professor, Department of Information Statistics, Andong National University, Andong 36729, Korea
3 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail:
Received June 13, 2023; Revised June 25, 2023; Accepted June 25, 2023.
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 copula is a multivariate distribution function that connects the marginal distributions of each variable with their joint distribution. It can be used to explain a diverse range of complex dependency structures of random variables, even those of high dimensionality. In practice, the correlation coefficient between two random variables can be influenced by other variables. This means that the relationship between the correlation coefficient and the explanatory variable is not always straightforward. In order to deal with this, we propose nonparametric Bayesian methods for variable selection and calculating variable importance. These methods use Bayesian Least absolute shrinkage and selection operator (Lasso) to identify the conditions under which the model can perform effectively. The performance of the model is then validated using simulation data. By incorporating these nonparametric Bayesian methods for variable selection and quantifying variable importance, we aim to enhance the modeling and analysis of complex dependency structures in copula. This approach holds promise in various fields, including finance, economics, and environmental studies, where understanding and accurately characterizing multivariate relationships are of utmost importance.
Keywords : Copula, correlation coefficient, nonparametric Bayesian analysis, shrinkage, transformation