A Unified Framework for Multiple Testing with Auxiliary Information: a Sample-splitting Approach

Highly developed information technologies constantly generate and store high-dimensional data that allow simultaneous testing of a large list of potential hypotheses. Such high-dimensional tests are often accompanied by some useful auxiliary information. Although several attempts have been made to incorporate the auxiliary information into statistical hypotheses tests, they are often specific to the problem studied and are implemented in a non-adaptive way. This brings new challenges and opportunities to statistical methodologies that perform inferential tasks in a unified framework that can incorporate the auxiliary information in an adaptive way. The proposed research project focuses on developing new approaches to jointly learning the structure or prior information from the data and to forming an accurate estimate of the false discovery proportion in large-scale multiple testing. This involves two fundamental issues: (1) The design of a large-scale testing system in the framework of a false discovery rate with auxiliary information; (2) the application of the unified framework to various scientific problems with specific structure or prior information. The project will be carried out with reference to broad range of applications where data and auxiliary information are available.