Statistical methods for large-scale inference

随着高通量技术在实践中越来越多地被采用，大规模统计推断通常在许多科学研究领域中进行，包括遗传学、神经成像、天文学等。更具体地说，在全基因组关联研究（GWAS）或神经影像学研究中，我们需要同时进行数百万个假设检验，每个假设检验都涉及单核苷酸多态性（SNP）或体素是否分别与表型相关。同时测试许多假设的挑战通常被称为多重测试问题。 这一提议的主要动机是认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，来自相关疾病的汇总统计量对于目标疾病的推断可以是高度信息化的。传统的多重检验方法没有考虑相关的辅助信息。在这个建议中，我们打算开发强大的多种测试方法，利用辅助信息，同时保持适当的错误控制。所开发的统计方法可以通过允许科学家充分利用现有的辅助信息来加速科学发现的进展。我们还计划通过利用检验统计量之间的相关性来开发强大的方法来分析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，发育障碍等。

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.