基于贝叶斯-Copula理论的高维离散变量相依性研究

项目名称： 基于贝叶斯-Copula理论的高维离散变量相依性研究

项目编号： No.11501355

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 方艳

作者单位： 上海对外经贸大学

项目金额： 18万元

中文摘要： 随着离散变量在各领域的不断丰富，其相依性的度量已成为众多学者关注的热点并取得了一定的研究成果，但是对于高维离散变量的相依性目前仍然缺乏严格有效的度量方法。为此，本课题首先通过连续拓展将离散变量转化为连续变量以简化高维离散变量相依性的研究过程；进而构建高维离散Copula模型来度量连续化后变量的相依性，并引入贝叶斯理论进行模型参数估计以解决传统方法导致的计算量庞大问题；最后运用我国车险投保人的理赔数据来检验所建模型的可行性和实用性。本研究的创新在于：兼顾单离散变量的“零膨胀”现象和过度离散现象构建高维离散Copula模型；引入Contrastive Divergence快速仿真算法拓展高维离散Copula模型的应用场景，从而突破传统贝叶斯方法（如，Gibbs Sampling）在高维数据应用上面临的计算瓶颈；借助实证分析实现理论与实际相结合，进一步丰富和完善我国的多元统计分析方法。

中文关键词： Copula；高维离散变量；相依性；贝叶斯理论；CD算法

英文摘要： With the enrichment of the discrete variables in various fields, its association studies have been a hot research topic and achieved certain results, however, there is still a lack of strict and effective measure for the associations among the high-dimensional discrete variables. As such, we first expand discrete variables to continuous variables in order to model the associations among the high-dimensional multivariate based on Copula. Then we propose a modeling paradigm including modeling, estimation and test procedures. Bayesian method is introduced to estimate model parameters since traditional estimation procedures are too slow. Finally the proposed method is used to explore the claim count dependency of Chinese auto insurances, which demonstrates the feasibility and applicability of our proposal. When modeling individual discrete variables, we allow for Zero-inflation and over-dispersion simultaneously. We find that the traditional Bayesian model estimators (e.g. Gibbs Sampling) still suffers the computation bottleneck when it comes to high-dimensional problems. Therefore, we introduce a more efficient simulation algorithm: Contrastive Divergence, which will extend the application territories of high-dimensional discrete copula and complement the existing statistical analysis for multivariate data. The empirical analysis demonstrates a perfect combination of statistical theory and application, then further improves the multivariate statistical analysis.

英文关键词： Copula;High-dimensional Discrete Variable;Association;Bayes Theory;Contrastive Divergence Algorithm