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

该项目旨在为高维数据开发适应性强大的测试程序，并将其应用于遗传学、基因组学和神经成像。由于最近生物技术的进步，人们收集了大量的高通量和高维的分子和成像数据，从而产生了一些新的和具有挑战性的统计问题。一个问题是，全基因组关联研究中的多基因测试如何被用来回答数百万个基因变异中的一些是否与阿尔茨海默病等复杂疾病有关。这个问题的答案对于发现与疾病相关的基因，从而制定有效的预防和治疗策略非常重要。关注严格的假设检验以避免错误发现，同时最大限度地增加真正发现的机会，对现代遗传学、基因组和其他基因组研究至关重要。这些方法将应用于与阿尔茨海默病相关的数据，目前还没有治愈方法，迫切需要更强大的分析方法来揭开潜在的生物学基础。研究生将参与计算工具的研究和开发，并将开发公开可用的软件包，供其他生物医学研究人员使用。这项研究将推动现代统计方法在高维数据假设检验和相关罕见事件评估方面的前沿。将开发强大的自适应方法来检验广义线性模型中的高维平均参数以及高维协方差矩阵结构。自适应测试统计量是基于高维高阶von Mise V统计量和U统计量构造的，对于稀疏、稠密以及中等稀疏或稠密的信号，对于灵活的渐近机制，它将提供一致的高功率。这项研究的另一个重点涉及在全基因组分子和神经成像数据的分析中具有挑战性和重要的罕见事件估计问题，其中通常需要高严格的统计显著性水平。为了评估这样的小概率，这项研究将导致理论上的尾部概率近似以及使用非标准测量变化技术的高效蒙特卡罗方法。

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.