Random Matrix Theory and High Dimensional Statistics

从广泛的科学研究中，包括基因组学、生物信息学、工程和气候研究，高维数据越来越多。对这些数据集的合理分析提出了许多统计上的挑战。它需要新的统计理论和方法，也需要新的技术工具。在这个合作研究项目中，研究人员将首先开发随机矩阵理论的结果和技术工具，然后采用统一的方法使用所开发的技术工具来研究高维统计中的几个重要问题以及在信号处理，物理和数学中的应用。本提案中概述的统计和科学目标是跨学科的，并将建立不同领域之间的联系-随机矩阵理论，高维统计，信号处理，物理和数学。这项研究还将为其他科学领域的研究人员收集和分析高维数据提供技术工具和方法。这些包括但不限于基因组学、生物统计学和电气工程。本计划所开发的程序和算法将会实施，而所开发的软件将会以开源代码的形式，连同相关的研究报告，在网上免费公开提供，以促进知识的传播。

High dimensional data are becoming increasingly available from a wide range of scientific investigations, including genomics, bioinformatics, engineering, and climate studies. Sound analysis of such datasets poses many statistical challenges. It calls for new statistical theory and methods as well as new technical tools. In this collaborative research project, the investigators will first develop results and technical tools in random matrix theory and then take a unified approach using the technical tools developed to study several important problems in high dimensional statistics as well as applications in signal processing, physics, and mathematics. The statistical and scientific objectives outlined in this proposal are interdisciplinary and will establish connections among different fields - random matrix theory, high dimensional statistics, signal processing, physics, and mathematics. The research will also provide technical tools as well as methodology, to researchers in other scientific fields who collect and analyze high dimensional data. These include, but are not limited to, genomics, biostatistics, and electrical engineering. The procedures and algorithms developed in this project will be implemented and softwares developed will be made freely and publicly available on the web as open sourcecode along with the associated research reports so as to facilitate the dissemination of knowledge.