Flexible Dependence Models for Multivariate Data

多元数据的灵活依赖模型

• 批准号: 435943-2013
• 负责人: Acar, Elif
• 金额: $ 1.46万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=636035
• 关键词: Flexible; Dependence; Models; Multivariate; Data

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.

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需要科学家专业知识指导下进行适当的统计分析。该研究计划重点在于提取和表征隐藏在多元数据中的相关信息。为了提取相关性，我们使用一种称为copula的机器，它将变量的边缘特征与它们的联合行为分开，为了描述依赖性，我们提出了非参数策略，这些策略足够灵活，可以捕获（1）动态条件依赖性，以及（2）大量变量之间的复杂相互关系。我们的方法学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，通过检测影响双胞胎或家族依赖的共同特征的双胞胎或家族研究，或通过指定不同危害程度之间的依赖关系来监测水文系统中的水质。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。