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

稀疏和微弱信号的检测是许多领域大数据分析的关键。最近的统计研究在揭示高斯均值模型和理想化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。可检测性边界描述了信号稀疏和微弱在二维相空间中的边界，低于这个边界的信号是渐近太弱和稀疏的，不能用任何统计方法来检测。某些统计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，这些理论模型与实际有意义的模型之间存在着很大的差距。在这个项目中，研究人员将统计理论扩展到处理广义线性模型框架下的弱、稀疏、相关和交互信号。研究人员开发了最佳测试程序，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。检测微弱和稀疏信号的统计理论和方法的发展是分析大数据的基础。这个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。这项研究对数据科学非常感兴趣，对许多应用程序都是至关重要的。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后，仍缺少复杂特征的遗传力。这项拟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遗传学研究不同，这项研究结合了严格的统计理论、该领域的第一手实践以及来自全基因组关联研究和下一代序列研究的尖端数据。拟议中的项目在寻找丢失的遗传性方面非常有希望。高度改进的基因检测技术将有助于发现更多人类复杂疾病的致病基因，这将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.