Bayesian Inference For C-Vine And Mixed Copula

With the development of the Internet and information industry,people are paying more attention to how to get meaningful information from a large amount of data and we are now really entering the era of data.However,the data on multiple indicators in real life are often correlated.Therefore,how to describe the dependent structure of multiple variables and make statistical inference and decision is an urgent problem.Vine Copula combines the Copula theory with the graphical modeling tool Vine.The multivariate joint distribution function is decomposed by the Pair-copula function,which can be used to describe the relative structure of the variable.This article will discuss the type of the Pair-copula based on the relationship between the Copula and the tail correlation coefficient.According to the possible situation of the tail-related structure,the eight categories of the Copula function are given,and the correlation between the two variables is captured.In order to take advantage of the prior information of the parameters,this paper studies the bayesian estimation method of C-Vine model.First,making reasonable assumptions about the relevant parameters in the Copula based on the relevant documentation of the Copula;Second,using the markov chain monte carlo algorithm to produce the posterior samples,which can be used to make statistical inferences about the parameters;Finally,the influence of the Pair-copula on the Vine model is given by random simulation,and the subsequent empirical analysis confirms that the C-Vine model based on the mixed Copula can capture the correlation between variables more flexibly.