Leveraging Covariate and Structural Information for Efficient Large-Scale and High-Dimensional Inference

大数据的扩散伴随着大量的问题，以假设检验的形式，这需要有效的方法来进行大规模和高维的推理。这些有影响力的方法必须同时涉及多个研究单元的统计分析。传统的同时推理过程通常假设不同单位的假设是可交换的。然而，在许多科学应用中，可以获得关于信号模式的外部协变量和结构信息。有效和准确地利用这些辅助信息将提高统计能力，并增强研究结果的可解释性。本研究的主旨是推进大规模和高维推理的统计方法和理论，特别注重将潜在有用的外部协变量和结构信息整合到推理过程中。本研究旨在发展创新的方法和理论，以解决大规模和高维推理中的几个重要问题。在项目1中，PI将引入一种新的多重检验程序，当存在大量外部协变量时，该程序可以自动选择相关协变量，以提高推断效率。在项目2中，PI将开发一个新的多重测试框架，它可以集成各种形式的结构信息。由于先验信息很少是完全准确的，一个特别的重点将是开发程序，是强大的错误指定/不完美的先验信息。在项目3中，PI应提出在具有边信息的高维回归中进行同时推理的新程序。统计工具将用于识别熟练的基金经理，评估气候场重建的表现，并以综合的方式分析基因组数据。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

The proliferation of big data is accompanied by a vast number of questions, in the form of hypothesis tests, which call for effective methods to conduct large-scale and high-dimensional inferences. These influential methods must involve statistical analysis on many study units simultaneously. Conventional simultaneous inference procedures often assume that hypotheses for different units are exchangeable. However, in many scientific applications, external covariate and structural information regarding the patterns of signals are available. Exploiting such side information efficiently and accurately will lead to improved statistical power, as well as enhanced interpretability of research results. The main thrust of this research is to advance statistical methodologies and theories for large-scale and high-dimensional inference with a particular focus on integrating potentially useful external covariate and structural information into inferential procedures. This research aims to develop innovative methodologies and theories to address several significant problems in large-scale and high-dimensional inference. In Project 1, the PI will introduce a new multiple testing procedure that can automatically select relevant covariates to improve the efficiency in inference when a large number of external covariates are available. In Project 2, the PI will develop a new multiple testing framework, which can integrate various forms of structural information. Because prior information is seldom perfectly accurate, a particular focus will be on developing procedures that are robust to misspecified/imperfect prior information. In Project 3, the PI shall propose new procedures for simultaneous inference in high-dimensional regressions with side information. The statistical tools will be used to identify skilled fund managers, assess the performance of climate field reconstructions, and analyze genomic data in an integrative way. Methods and computer code developed will be made publicly available.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.