Statistical methods for large-scale inference

随着高通量技术在实践中越来越多的应用，大规模的统计推断在许多科学研究领域，包括遗传学、神经影像学、天文学等领域都得到了广泛的应用。更具体地说，在全基因组关联研究（GWAS）或神经成像研究中，我们需要同时进行数百万个假设检验，每个假设检验分别涉及单个核苷酸多态性（SNP）或体素是否与表型相关。同时测试多个假设的挑战通常被称为多重测试问题。这个提议的主要动机是意识到科学调查很少孤立地进行，文献中通常有相关的信息和相关的实验。例如，相关疾病的汇总统计数据对于推断目标疾病具有很高的信息量。传统的多重测试方法没有考虑相关的辅助信息。在本方案中，我们打算利用辅助信息开发强大的多重测试方法，同时保持适当的误差控制。所开发的统计方法可以使科学家充分利用现有的辅助信息，从而加速科学发现的进展。我们还计划开发强大的方法来利用测试统计量之间的相关性来分析GWAS。我们的方法的应用可以促进我们对许多人类复杂特征和疾病的遗传基础的理解，包括身高、肥胖、风湿性疾病、发育障碍和许多其他疾病。

As the high-throughput technologies are increasingly adopted in practice, large-scale statistical inference is commonly conducted in many scientific research areas, including genetic, neuroimaging, astronomy, and many others. More specifically, in genome-wide association studies (GWAS) or neuroimaging studies, we need to conduct millions of hypothesis tests simultaneously, each of which concerns whether a single nucleotide polymorphism (SNP) or voxel is associated with a phenotype, respectively. The challenge of simultaneously testing many hypotheses is commonly referred to as the multiple testing problem. This proposal is mainly motivated by the realization that scientific investigations are rarely conducted in isolation, and there are typically relevant information and related experiments in the literature. For example, the summary statistics from a related disease can be highly informative for the inference of a target disease. Traditional multiple testing methods do not consider the relevant auxiliary information. In this proposal, we intend to develop powerful multiple testing methods by utilizing the auxiliary information while maintaining proper error control. The statistical methods developed can accelerate the progress of scientific discoveries by allowing scientists to fully utilize existing auxiliary information. We also plan to develop powerful methods to analyze GWAS by taking advantage of the correlations among test statistics. The applications of our methods can advance our understanding of the genetic basis of many human complex traits and diseases, including height, obesity, rheumatic diseases, developmental disorders, and many others.