Flexible Dependence Models for Multivariate Data

在过去的三十年里，从宇宙的扩张到人类基因组的完成，见证了令人着迷的科学发现。这些只能在一个世纪前的科幻小说领域中想象出来。现代技术在这些成就中发挥了关键作用，使科学家能够收集难以获得的海量数据。然而，将数据中的信息转换成有意义的知识一直是我们在科学家的专业知识指导下进行适当的统计分析的功劳。本研究的重点是提取和刻画隐藏在多变量数据中的依赖信息。为了提取依赖信息，我们使用了一种称为Copula的机制，它将变量的边缘特征与它们的联合行为分开，为了刻画依赖关系，我们提出了足够灵活的非参数策略，这些策略足够灵活地捕捉(1)动态条件依赖关系，(2)大量变量之间的复杂相互关系。我们的方法论贡献将极大地扩展基于Copula的依赖模型在应用中的能力和灵活性。例如，所提出的方法可以用于揭示骨骼和肌肉相互作用的骨骼解剖学研究，通过检测影响同卵双胞胎或家庭依赖的共同特征来进行双胞胎或家庭研究，或者通过指定不同危险级别之间的依赖关系来在水文系统中进行水质监测。特别是，这项研究将对马尼托巴大学马尼托巴五大湖项目的水质测量的条件依赖性和联合依赖性进行详细的分析。

The last three decades have witnessed fascinating scientific discoveries, from the expansion of our universe to the completion of human genome. These could only be imagined in the realms of science fiction just a century ago. Modern technology plays a pivotal role in these achievements by enabling scientists to collect hard-to-reach data and in massive amounts. However, converting the information in data to meaningful knowledge is always what we are indebted to proper statistical analysis, directed by scientists' expertise.This research program focuses on extracting and characterizing dependence information concealed in multivariate data.To extract dependence, we use a machinery called copula that separates marginal characteristics of variables from their joint behaviour, and to characterize dependence we propose nonparametric strategies that are flexible enough to capture (1) dynamic conditional dependencies, and (2) complex interrelations among a large number of variables. Our methodological contributions will greatly extend the capabilities and flexibility of copula-based dependence models in applications.The proposed methods can be used to shed light into, for instance, studies of skeletal anatomy by revealing bone and muscle interactions, twin or family studies by detecting the shared characteristics that affect co-twin or familial dependence, or water quality monitoring in hydrological systems by specifying dependencies between the level of different hazards. In particular, this research will offer elaborate analyses of conditional and joint dependencies of water-quality measurements to the Manitoba Great Lakes Project of the University of Manitoba.