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

该研究项目旨在创建用于大规模多重比较的新工具。 特别是，研究人员在频域开发新的工具，以解决这一领域的问题。该项目包括（a）。介绍傅立叶分析作为多重比较的工具。研究者致力于通过利用傅立叶分析的力量来推动该领域的边界。傅立叶分析在许多科学领域中被反复证明是一种强有力的工具，但很少被用于大规模多重比较领域。（B）。开发实际可行的工具，并为研究工具的最佳性奠定理论框架。（c）.扩展和应用开发的方法和理论，以分析在各个科学领域产生的大量数据，包括比较基因组杂交（CGH）， 宇宙学和天文学，以及基因微阵列。 现代数据采集通常会在许多科学领域产生大量数据集，例如基因组学，天文学，功能性磁共振成像（fMRI）和图像处理。 其愿景是，海量数据分析的进步将使来自各个领域的科学家能够快速提取他们所需的信息，同时， 有利于统计学科与理论和方法的更广泛的范围，但也与自然和科学的更深入的理解。该项目通过引入解决问题的新思路，开发新工具和新理论，并将工具应用于其他科学领域，包括但不限于比较基因组杂交（CGH），宇宙学和天文学以及基因微阵列，从而推动了该领域的边界。

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.