Multivariate models and inference

超越多元正态性假设的多元模型越来越多地被使用。 Copula函数是构造多元模型的一种工具，并且在越来越多的科学领域得到了广泛的应用。 因此，这一领域的研究是基础科研以及应用驱动。 Web of Science数据库显示了许多标题中包含Copula的文章; Copula应用较多的领域包括：（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。 任何非高斯依赖性的方法对于大型/巨大的数据集将变得更加重要，对于这些数据集，可以更容易地检测到与多元正态性的偏差。当存在尾部依赖或尾部相对于高斯联合尾部不对称时，通常需要从多元正态模型扩展到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大损失的风险。最近和未来研究的主要目标是进一步发展多变量模型和推断/计算程序的多变量非正态响应与协变量。 随着大量的变量，它是可取的，有可解释的多变量模型与简约的依赖结构和灵活的尾部行为。 各种依赖模型通过图形模型进行解释，图形模型显示不同变量如何联系以及存在条件独立关系的地方。 软件已经或正在开发，以处理非常大的尺寸。 响应类型包括二元、有序分类、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（多代大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）金融资产收益。

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.**