Multivariate models and inference

超越多元正态假设的多元模型正越来越多地被使用。Copula是构建多元模型的一种工具，在越来越多的科学领域得到了广泛的应用。因此，这一领域的研究既是基础科学研究，也是应用驱动的研究。科学网数据库显示了许多以Copula为标题的文章；有许多Copula应用的领域包括(I)商业、经济和金融，(Ii)气候、环境和水文学，(Iii)工程和可靠性，(Iv)农业、林业和生物统计学。对于大数据集/巨型数据集，任何用于非高斯相关性的方法都将变得更加重要，对于这些数据集，对多变量正态分布的偏差可以更容易地检测到。 当存在尾部相关性或相对于高斯联合尾部的尾部不对称性时，通常需要从多变量正态模型扩展到Copula模型。在保险或金融风险分析中，使用经典的多元正态理论会低估联合巨额损失的风险。 最近和未来一些研究的主要目标是进一步发展具有协变量的多变量非正态响应的多变量模型和推理/计算程序。在变量数量较多的情况下，需要具有简约依赖结构和灵活尾部行为的可解释的多变量模型。各种依赖模型通过图形模型进行解释，这些模型显示了不同变量是如何联系在一起的，以及在哪里存在条件独立关系。已经或正在开发软件来处理非常大的维度。响应类型包括二进制、序数分类、计数、生存、重尾、极值。数据的例子包括(A)医学遗传学应用中的家族数据(扩展的多代家庭中每个成员的测量)，(B)心理测量学应用中的项目反应数据，(C)金融资产回报。

Multivariate models that go beyond the assumption of multivariate normality are increasingly being used. Copulas are one tool for constructing multivariate models, and copulas are used in more and more scientific areas. So this area of research is basic scientific research as well as application-motivated. The Web of Science database shows many articles with copula in the title; areas with many copula applications include (i) business, economics and finance, (ii) climate, environment and hydrology, (iii) engineering and reliability, (iv) agriculture, forestry and biostatistics. Any methodology for non-Gaussian dependence will becomes more important with large/huge data sets for which deviations from multivariate normality can be more easily detected. The extension from multivariate normal models to copula models is typically needed when there is tail dependence or tail asymmetry relative to Gaussian joint tails. In insurance or financial risk analysis, use of classical multivariate normal theory would underestimate risks from jointly large losses. The main objectives of some recent and proposed future research is to further develop multivariate models and inference/computing procedures for multivariate non-normal response with covariates. With a larger number of variables, it is desirable to have interpretable multivariate models with parsimonious dependence structures and flexible tail behaviour. The various dependence models have interpretations via graphical models which show how different variables are linked and where there are conditional independence relations. Software has been or is being developed to handle very large dimensions. Response types include binary, ordinal categorical, count, survival, heavy-tailed, extreme value. Examples of data include (a) familial data (measurements for each member of an extended multi-generation family) in medical genetics applications, (b) item response data in psychometrics applications, (c) financial asset returns.