Optimal tests for weak, sparse, and complex signals with application to genetic association studies

在许多领域，稀疏和微弱信号的检测是分析大数据的关键。近年来的统计研究在揭示高斯均值模型和理想线性回归模型下的可检测性边界方面取得了显著的理论进展。可检测性边界表示信号在二维相空间中的稀疏度和弱度边界，在此边界以下的信号渐近过弱和稀疏，任何统计方法都无法检测到。某些统计数据对于这些模型来说是最优的，因为它们达到了可靠信号检测的边界（即最低要求）。然而，这些理论模型与有实际意义的模型之间存在着显著的差距。在这个项目中，研究者将统计理论扩展到在广义线性模型的框架下处理弱、稀疏、相关和交互的信号。研究人员开发了最佳的测试程序，以解决全基因组关联研究和下一代序列研究中的现实数据特征。微弱和稀疏信号检测的统计理论和方法的发展是分析大数据的基础。该项目的目标是扩展统计理论研究，以解决与定量或分类反应相关并相互影响的复杂信号。这项研究在数据科学中引起了极大的兴趣，对许多应用都至关重要。例如，当前遗传学研究的一个令人困惑的问题是，即使在确定了许多遗传因素之后，复杂性状的遗传能力仍然缺失。这项提议的工作专门针对那些尚未发现的隐藏疾病基因的特征。与一些基于启发式论证的基因研究不同，本研究结合了严格的统计理论的力量，实地的第一手实践，以及全基因组关联研究和下一代序列研究的前沿数据。在寻找缺失的遗传性方面，拟议的项目是非常有希望的。高度改进的基因检测技术将有助于识别更多复杂人类疾病的致病基因，从而有助于阐明疾病的发病机制和设计靶向治疗方法，从而对提高生活质量产生深远影响。

Detection of sparse and weak signals is a key for analyzing big data in many fields. Recent statistical research has made celebrated theoretical progress in revealing the detectability boundaries under the Gaussian means model and an idealized linear regression model. Detectability boundary illustrates the border in the two-dimensional phase space of signal sparsity and weakness, below which the signals are asymptotically too weak and sparse to be detectable by any statistical methods. Certain statistics are optimal for these models in the sense that they reach the boundary (i.e., the least requirements) for reliable signal detection. However, there are significant gaps between these theoretical models and practical meaningful models. In this project, the investigators extend statistical theory to handle weak, sparse, correlated, and interactive signals under the framework of generalized linear models. The investigators develop optimal testing procedures to address the realistic data features in genome-wide association studies and next-generation sequence studies. Statistical theory and methodology development for the detection of weak and sparse signals is foundational for analyzing big data. The goal of this project is to extend statistical theoretical study to address complex signals that are correlated and interactively influential to quantitative or categorical responses. This study is of great interest in data science and is critical to many applications. For example, one perplexing problem of current genetic studies is the missing heritability of complex traits even after many genetic factors have been identified. The proposed work specifically addresses the features of those hidden disease genes yet to be discovered. Unlike some genetic studies based on heuristic arguments, this research combines the power of rigorous statistical theory, first-hand practices in the field, and cutting-edge data from genome-wide association studies and next-generation sequence studies. The proposed project is highly promising in the hunt for the missing heritability. Highly improved gene-detection techniques will help to identify more causative genes of complex human diseases, which will lead to the elucidation of disease pathogenesis and design of targeted therapeutics, thus have a far-reaching impact on improving quality of life.