Controlling Positive False Discovery Rate with Power

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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.