Collaborative Research: Adaptive Testing and Rare-Event Analysis of High-Dimensional Data

协作研究：高维数据的自适应测试和罕见事件分析

• 批准号: 1712717
• 负责人: Gongjun Xu
• 金额: $ 12万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-15 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712717&HistoricalAwards=false
• 关键词: Collaborative; Research; Adaptive; Testing; Rare; Collaborative; Research; Adaptive; Testing; Rare

This project aims at developing adaptively powerful testing procedures for high-dimensional data with applications in genetics, genomics and neuroimaging. Due to recent biotechnological advances, large amounts of high-throughput and high-dimensional molecular and imaging data have been collected, resulting in a number of new and challenging statistical questions. One question is how polygenic testing in genome-wide association studies (GWAS) may be used to answer whether some of the millions of genetic variants are associated with a complex disease like Alzheimer's disease. The answer to this question is important to uncovering disease-related genes, and thus developing effective prevention and treatment strategies. The focus on rigorous hypothesis testing to avoid false discoveries, while maximizing the chance for true discoveries, is critical to modern genetic, genomic and other omic studies. The methods will be applied to data related to Alzheimer's disease, for which currently there is no cure, and more powerful analysis methods are urgently needed to unravel the underlying biology. Graduate students will be involved in the conduct of the research and development of the computational tools, and publicly available software packages will be developed for use by other biomedical researchers.This research will advance the frontiers of modern statistical methodology in hypothesis testing with high-dimensional data and related rare event assessment. Powerful adaptive methods for testing high-dimensional mean parameters in generalized linear models as well as high-dimensional covariance matrix structures will be developed. The adaptive test statistics are constructed based on high-dimensional high-order von Mises V-statistics and U-statistics, and will provide uniformly high power against sparse, dense, as well as moderately sparse or dense signals for flexible asymptotic regimes. Another thrust of the research deals with the challenging and important rare-event estimation problem in analysis of genome-wide molecular and neuroimaging data, where a high stringent statistical significance level is usually needed. To evaluate such small probabilities, the research will lead to theoretical tail probability approximations as well as efficient Monte Carlo methods using non-standard change-of-measure techniques.

该项目旨在为具有遗传学，基因组学和神经影像学应用的高维数据开发适应性强大的测试程序。 由于最近的生物技术进步，已经收集了大量的高通量和高维分子和成像数据，从而导致了许多新的且具有挑战性的统计问题。 一个问题是，全基因组关联研究（GWAS）中的多基因测试可以用来回答数百万个遗传变异中的某些遗传变异是否与阿尔茨海默氏病等复杂疾病有关。 这个问题的答案对于揭示与疾病相关的基因，从而制定有效的预防和治疗策略很重要。对严格的假设检验的关注，以避免发现错误发现，同时最大程度地提高了真正发现的机会，这对于现代遗传，基因组和其他OMIC研究至关重要。 这些方法将应用于与阿尔茨海默氏病有关的数据，目前尚无治愈方法，并且迫切需要更强大的分析方法来揭示潜在的生物学。研究生将参与计算工具的研究和开发的行为，并将开发其他生物医学研究人员使用的公开软件包。这项研究将通过高维数据和相关罕见的稀有事件评估来推动现代统计方法论的前沿。将开发用于测试普通线性模型中高维平均参数以及高维协方差矩阵结构的强大自适应方法。 自适应测试统计数据是基于高维的高阶von Mises V统计和U统计量来构建的，并将为稀疏，密集以及中等稀疏或密集的信号提供统一的高功率，以实现灵活的渐近性制度。研究的另一个力量涉及在基因组分子和神经影像学数据的分析中具有挑战性且重要的稀有事实估计问题，其中通常需要高严格的统计显着性水平。为了评估如此小的概率，研究将导致理论上的尾巴概率近似以及有效的蒙特卡洛方法，使用非标准的量化技术。