RTG: Geometry and Statistics

分析不同种类数据的统计工具变得越来越重要，这既导致数据科学这一新领域的突出，也导致各级需要更多的研究人员。该项目将培养该领域的下一代领导者。统计与几何研究培训小组(RTG)将为不同学术水平的学生提供通道：该计划将资助本科生研究项目，让学生对研究感到兴奋，这样他们就会看到自己在统计学领域追求研究生职业生涯。研究生将有机会在暑期开设自己的课程，为他们提供通往学术生涯的大门，因为他们认为自己会成为老师和导师。新设立的三个博士后职位将培养在新兴数据科学领域具有较强量化背景的博士后。将所有参与者联系在一起的共同主题是统计学中几何方法的使用及其在现代生物学中对高维复杂数据的应用。该计划旨在最大限度地提供指导和互动机会，通过统计学和几何及其在生物学中的应用方面的高度相关的课程和工作组，为每个参与者提供关于统计学最新水平的广泛视角。该计划的一个显著特点是，它将发展参与者的智力广度以及指导和沟通技能。该项目将允许更多的美国学生通过参与数据科学来补充他们对数学、应用数学或计算机科学的兴趣，这是当前许多信息技术领域的关键需求。在分析异质数据方面取得的进展将通过改进可视化和几何表示以及评估基于图像或网络数据做出决策的不确定性水平的可能性来加强医学发现。应用领域将包括计算解剖学、神经科学、免疫学和基因组学。开发的方法将扩展多变量统计，其中特定的度量(如Fisher信息度量、马氏距离或L1)已经提供了成功的投影和几何表示。微分几何将提供一个严格的框架，使之能够纳入局部信息。将与计算几何学家、统计学家和数学家合作解决使用非欧几里得变种的统计数据提出的问题。在几何、统计和信息科学方面创建正式的计划将为课程带来新的活力和重点，鼓励有数学基础的学生应对应用数据分析挑战。这一倡议的一个重要组成部分是与妇女和少数族裔学生进行接触。该计划开发的材料和工具将包括用R编程语言编写的开源可视化和近似程序包。

Statistical tools for the analysis of heterogeneous data have become increasingly important, leading both to the prominence of the new field of data science and to a need for more researchers at all levels. This project will train the next generation of leaders in the field. The Statistics and Geometry Research Training Group (RTG) will provide gateways for students at the various academic levels: The program will fund undergraduate research programs to get students excited by research so that they see themselves pursuing a graduate career in statistics. Graduate students will have the opportunity to develop their own classes in the summer, providing them with a gateway to an academic career as they see themselves becoming teachers and mentors. Three newly created postdoctoral positions will train doctoral recipients with a strong quantitative background in the emerging field of data science. The common theme linking all the participants will be the use of geometric methods in statistics and their applications to high dimensional complex data in modern biology. The program is structured to maximize mentoring and interaction opportunities, providing each participant with a broad perspective of the state of the art in statistics through highly relevant courses and working groups in statistics and geometry and their applications to biology. A salient feature of the program is that it will develop both the intellectual breadth as well as the mentoring and communication skills of the participants. The program will allow more U.S. students to supplement their interests in mathematics, applied mathematics, or computer science with involvement in data science, which is a crucial current need in many areas of information technology. The progress made in the analysis of heterogeneous data will enhance medical discovery through improved visualization and geometrical representations as well as the possibility to assess levels of uncertainty in making decisions based on images or network data. Domains of application will include computational anatomy, neuroscience, immunology, and genomics. The methods developed will extend multivariate statistics where specific metrics (such as Fisher's Information metric, Mahalanobis distance, or L1) have already provided successful projections and geometric representations. Differential geometry will provide a rigorous framework that enables the incorporation of local information. The questions raised by using statistics on non-Euclidean varieties will be addressed in collaboration with computational geometers, statisticians, and mathematicians. Creating formal initiatives in geometry, statistics, and information science will bring new energy and focus into the curriculum, with mathematically grounded students encouraged to attack applied data analytic challenges. A key component of this initiative is outreach to women and minority students. Material and tools developed by the program will include open source visualization and approximations packages written in the R programming language.