Flexible Dependence Models for Multivariate Data

在过去的三十年里，从宇宙的膨胀到人类基因组的完成，我们见证了令人着迷的科学发现。这些只能在世纪前的科幻小说中想象。现代技术在这些成就中发挥了关键作用，使科学家能够收集大量难以获得的数据。然而，将数据中的信息转化为有意义的知识，始终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结果。 该研究项目的重点是提取和表征隐藏在多变量数据中的依赖信息。为了提取依赖，我们使用一种称为copula的机器，将变量的边际特征从它们的联合行为中分离出来，为了表征依赖，我们提出了足够灵活的非参数策略，以捕获（1）动态条件依赖，以及（2）大量变量之间的复杂相互关系。我们的方法的贡献将大大扩展Copula依赖模型在应用中的能力和灵活性。 所提出的方法可以用来阐明，例如，骨骼解剖学研究揭示骨骼和肌肉的相互作用，双胞胎或家庭的研究，通过检测共同的特点，影响双胞胎或家庭的依赖性，或水质监测水文系统指定的依赖性之间的水平不同的危害。特别是，这项研究将提供详细的分析条件和联合依赖的水质测量的马尼托巴五大湖项目的马尼托巴大学。

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.