New Theory and Methodology for Large-Scale Multiple Testing

大规模多重检验是现代统计学中一个重要而迅速发展的领域。提出的研究重点是新的理论、方法和计算算法，以解决该领域的基本问题和新的挑战。研究者开发了新的概念、数据驱动方案和坚实的理论，这些理论有望提高统计效率，并为大规模研究中的同步推断奠定基础，特别是当异质性、依赖性和其他复杂结构存在时。本研究的主要内容包括：(i)在多重检验中同时纳入统计显著性和效应量的概念，以及在异方差模型中识别大型非零效应的新方法；（ii）利用空间依赖性的策略和在隐马尔可夫随机场中检验相关假设的新方法；(3)假设集合分组策略和检验多组重要变量显著性的新方法；（iv）发现边界和有效筛选的概念，以及通过构建最优大小和自适应未知稀疏度的子集来降低维度的数据驱动方法。该研究对全基因组关联研究、时程微阵列实验、环境研究中的疾病制图、气候建模和医学成像研究等许多科学应用具有重要影响。提案中概述的多种检测和筛选方法将提高在复杂情况下同时决策的质量，产生更多可解释和可重复的科学结果，大大节省大规模研究的成本，从而有助于实现以精确、快速和经济有效的方式了解复杂系统或人类疾病的潜在机制的最终目标。将开发方便用户使用的软件，并免费提供给公众使用。研究成果将通过出版物、讨论会和讲习班传播。研究者致力于鼓励代表性不足的群体参与科学，并通过开发新课程，以及通过指导和培训学生在统计学前沿与重要的卫生科学应用领域工作，将拟议的研究纳入教育活动。

Large-scale multiple testing is an important and rapidly growing area in modern Statistics. The proposed research focuses on new theories, methodologies and computational algorithms to address the fundamental questions and new challenges in this field. The investigator develops new concepts, data-driven schemes and solid theories that promise to improve the statistical efficiency and lay the foundation for simultaneous inferences in large-scale studies, especially when heterogeneity, dependence and other complex structures are present. The major components of the proposed research include: (i) the concept of simultaneously incorporating statistical significance and effect size in multiple testing and a new approach to identifying large non-null effects in heteroscedastic models; (ii) the strategy of exploiting spatial dependency and a new approach to testing correlated hypotheses in a hidden Markov random field; (iii) the strategy of grouping hypotheses in sets and a new approach to testing the significance of multiple groups of important variables; and (iv) the concepts of discovery boundary and effective screening, and a data-driven approach to reducing dimensionality by constructing subsets that are optimal in size and adaptive to unknown sparsity. The proposed research has significant impact on many scientific applications such as genome-wide association studies, time-course microarray experiments, disease mapping in environmental studies, climate modeling, and medical imaging studies. The multiple testing and screening methods outlined in the proposal will improve the quality of simultaneous decision-making in complicated situations, yield more interpretable and reproducible scientific results, lead to great savings in costs in large-scale investigations, and hence help achieve the ultimate goal of understanding the underlying mechanisms in complex systems or human diseases in a precise, fast and cost-effective way. User-friendly software will be developed and made freely available for public use. Research results will be disseminated through publications, seminars and workshops. The investigator is committed to encouraging the participation of under-represented groups in science, and to integrating the proposed research into educational activities through developing new courses, and through mentoring and training students to work on the frontiers in Statistics with important health science applications.