Controlling Positive False Discovery Rate with Power

本研究计划旨在发展理论和方法工具，以提高错误率控制和多假设检验的能力。调查的核心是错误发现率（FDR）及其重要的相对值，即所谓的阳性FDR （pFDR）。首先，为了更客观地评估被拒绝的零值或发现，PI将开发评估多重测试的pFDR的方法，以及设置测试统计标准的方法，以确保他们有足够的信息来实现所需的pFDR控制。其次，PI将开发基于多元统计的FDR控制。尽管在许多领域广泛使用多元统计进行多重检验，但在当前关于FDR控制的文献中，关于这一主题的工作很少。PI将开发包含多元统计的不同的FDR控制程序，并研究如何有效地组合统计中的信息，以实现最优功率的pFDR控制。多重假设检验为现代科学和技术领域的大量数据分析和知识发现提供了统计基础，包括神经科学、脑成像、基因组学和图像处理。这些领域的一个基本挑战是在避免错误发现的同时获得真正的发现。该项目将产生各种工具来实现这一目标。它将使研究人员能够更仔细地评估发现，并避免数据收集和分析中的潜在缺陷。此外，它将为研究人员提供大量的统计方法，以更有效地找到真正的发现。

This research proposal aims to develop theoretical and methodological tools to improve error rate control and power for multiple hypothesis testing. The centerpiece of the investigation is the False Discovery Rate (FDR) and its important relative, the so-called positive FDR (pFDR). First, in order to evaluate rejected nulls or discoveries more objectively, the PI will develop methods to estimate the pFDR for multiple testing as well as methods to set criteria for test statistics in order to make sure they have enough information to attain desired pFDR control. Second, the PI will develop FDR control based on multivariate statistics. Although using multivariate statistics for multiple testing is widely seen in many areas, there has been little work on this topic in the current literature on FDR control. The PI will develop different FDR controlling procedures that incorporate multivariate statistics and investigate how to combine the information in the statistics effectively in order to achieve pFDR control with optimal power.Multiple hypothesis testing provides a statistical foundation for massive data analysis and knowledge finding in a wide range of areas of modern science and technology, including neuroscience, brain imaging, genomics and imagery processing. A fundamental challenge in these areas is to obtain true discoveries while avoiding false discoveries. The project will generate various tools to reach this goal. It will enable researchers to evaluate discoveries more carefully and to avoid potential pitfalls in their data collection and analysis. Moreover, it will provide researchers with a large collection of statistical methods to find true discoveries more efficiently.