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且发展迅速的领域。拟议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。研究人员开发新的概念，数据驱动的方案和坚实的理论，这些理论有望提高统计效率，并为大规模研究中的同时推理奠定基础，特别是当存在异质性，依赖性和其他复杂结构时。该研究的主要内容包括：（i）在多重检验中同时引入统计显著性和效应量的概念，以及识别异方差模型中大的非零效应的新方法;（ii）利用空间依赖性的策略，以及在隐马尔可夫随机场中检验相关假设的新方法; ㈢将假设分组的战略和检验多组重要变量的重要性的新方法;以及（iv）发现边界和有效筛选的概念，以及一种数据驱动的方法，通过构建大小最优且适应未知稀疏性的子集来降低维度。该研究对许多科学应用具有重要影响，如全基因组关联研究，时间过程微阵列实验，环境研究中的疾病定位，气候建模和医学成像研究。该提案中概述的多种测试和筛选方法将提高复杂情况下同时决策的质量，产生更多可解释和可复制的科学结果，从而大大节省大规模调查的成本，从而有助于以准确，快速和具有成本效益的方式实现了解复杂系统或人类疾病的潜在机制的最终目标。将开发方便用户的软件，免费提供给公众使用。研究成果将通过出版物、研讨会和讲习班传播。调查员致力于鼓励代表性不足的群体参与科学，并通过开发新的课程，并通过指导和培训学生在统计学前沿工作，将拟议的研究纳入教育活动中，具有重要的健康科学应用。

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.