CAREER: Inferences on Large-Scale Multiple Comparisons: The Temptation of the Fourier Kingdom

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This research project is to create new tools for large-scale multiple comparisons. In particular, the investigator develops new tools in the frequency domain to tackle problems in this field. The project includes (a). Introduce Fourier analysis as a tool for multiple comparisons. The investigator devotes to push the boundary of the field by harnessing the power of Fourier analysis. The Fourier analysis has been repeatedly proven to be a powerful tool in many scientific areas, but has seldom been used in the field of large-scale multiple comparisons. (b). Develop practically feasible tools, and lay out theoretic frameworks for studying the optimality of the tools. (c). Extend and apply the developed methodology and theory to the analysis of massive data generated in various scientific fields, including comparative genomic hybridization (CGH), cosmology and astronomy, and gene microarray. Modern data acquisition routinely produces massive data sets in many scientific areas, e.g. genomics, astronomy, functional Magnetic Resonance Imaging (fMRI), and image processing. The vision is that advances in massive data analysis will enable scientist from various fields to quickly extract the information they need, and at the same time, benefit the statistical discipline both with a broader scope of theory and methodology but also with a deeper understanding of nature and science. The project pushes the boundary of the field by introducing new ideas for problem solving, developing new tools and novel theory, and applying the tools to other scientific fields including but not limited to comparative genomic hybridization (CGH), cosmology and astronomy, and gene microarray.