Nonparametric Bayesian copula modeling for shrinkage through the transformation

초록

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.

키워드