Multivariate models and inference

超越多元正态性假设的多元模型被越来越多地使用。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应用。所以这个领域的研究是基础科学研究，也是应用驱动的。Web of Science数据库显示，许多文章的标题中都有copula；具有许多copula应用的领域包括(i)商业、经济和金融，（ii）气候、环境和水文，（iii）工程和可靠性，（iv）农业、林业和生物统计学。对于更容易检测到偏离多元正态性的大型/庞大数据集，任何非高斯相关性的方法都将变得更加重要。******当相对于高斯联合尾存在尾依赖或尾不对称时，通常需要将多元正态模型扩展到联结模型。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共同巨大损失的风险。******一些最近和提出的未来研究的主要目标是进一步开发多变量模型和多变量非正态响应的推理/计算程序。对于大量的变量，需要具有简洁的依赖结构和灵活的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，这些图形模型显示了不同变量是如何联系在一起的，以及哪里存在条件独立关系。软件已经或正在开发，以处理非常大的维度。响应类型包括二进制、有序分类、计数、生存、重尾、极值。数据示例包括(a)医学遗传学应用中的家族数据（一个扩展的多代家庭中每个成员的测量值），(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.**