Dependence Models for Complex and Massive Data

过去几十年的科学和技术进步带来了数据数量和复杂性的显着增长。这为统计研究带来了许多挑战和机遇，无论是作为一门跨学科还是基础学科。 在许多应用中，了解所收集数据中的依赖机制对于深入了解潜在生物或物理过程的本质至关重要。然而，大量数据的统计分析往往限于单变量特征，缺乏对感兴趣的结果之间的多变量依赖关系的理解。另一方面，在中小规模的研究中，手动定制的多变量模型可能并不总是足以解释数据中复杂性的各种来源。这项研究计划通过贡献新的多变量建模策略来解释统计依赖性，从而弥合了这两个方面。研究计划的第一个主题是解决中小规模研究中研究设计和数据收集过程中产生的数据复杂性，特别关注不完整的数据设置。这些包括（i）临床研究中的删失生存数据，（ii）物理和生物医学应用中的错误测量数据，（iii）调查数据中出现的潜在变量，以及（iv）神经成像和纵向研究中缺失或不等距数据。这些方面将在本研究中使用广泛的基于Copula的依赖模型，如条件Copula，藤蔓Copula和因子Copula来解决。该研究计划的第二个主题解决了分析来自大型多中心研究联盟的高通量数据的一些统计挑战。具体而言，我们贡献了多变量建模策略和新的荟萃分析方法，以揭示涉及模式生物的多中心实验中的跨表型依赖性。根据这项研究计划开发的统计工具将有助于评估和确保科学实验的可重复性。此外，该研究计划将提供几个机会，培养学生的方法，应用和计算方面，并让他们参与尖端的生物医学，临床和遗传研究。

Scientific and technological advancements over the last few decades have brought a significant growth in the amount and complexity of data. This invited many challenges and opportunities for statistical research, both as an interdisciplinary and fundamental discipline. In many applications, understanding the dependence mechanisms in the collected data is crucial to bring insights into the nature of the underlying biological or physical process. However, statistical analyses of massive amounts of data are often limited to univariate features, lacking an understanding of multivariate dependencies among outcomes of interest. On the other hand, in small- to medium-scale studies, manually tailored multivariate models may not always sufficiently account for the various sources of complexity in the data. This research program bridges these two aspects by contributing novel multivariate modeling strategies to account for statistical dependence. The first theme of the research program addresses data complexities arising from study design and data collection process in small- to medium-scale studies, with a particular focus on incomplete data settings. These include (i) censored survival data in clinical studies, (ii) mismeasured data in physical and biomedical applications, (iii) latent variables arising in survey data, and (iv) missing or unequally spaced data in neuroimaging and longitudinal studies. These aspects will be tackled in this research using a wide range of copula-based dependence models such as conditional copulas, vine copulas and factor copulas. The second theme of this research program addresses some of the statistical challenges in analyzing high-throughput data from large-scale multi-center research consortia. Specifically, we contribute multivariate modeling strategies and novel meta-analysis methods to shed light into cross-phenotype dependencies in multi-center experiments involving model organisms. Statistical tools developed under this research program will help evaluate and ensure reproducibility in scientific experiments. Moreover, this research program will provide several opportunities to train students on methodological, applied and computational aspects, and to involve them in cutting-edge biomedical, clinical and genetic research.