Distance Correlation Measures, with Applications to Astrophysical Databases and Diffusion Tensor Imaging

距离相关测量，及其在天体物理数据库和扩散张量成像中的应用

• 批准号: 1309808
• 负责人: Donald Richards
• 金额: $ 19.5万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-15 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1309808&HistoricalAwards=false
• 关键词: Distance; Correlation; Measures; Applications; Astrophysical

The principal investigator (PI) will conduct theoretical and applied research on distance correlation methods, with applications to high-dimensional astrophysical databases. This research will be accomplished with co-authors in statistics and astronomy, and with graduate students. The PI and a Co-PI will develop Hankel transforms for distributions on matrix spaces and apply the results to develop goodness-of-fit testing procedures for data consisting of symmetric positive definite random matrices. The PI and a Co-PI will analyze high-dimensional astrophysical databases on galaxy clusters to identify associations and correlations between multiple astrophysical variables. Research on distance correlation measures for mixtures of Gaussians and general heavy-tailed distributions will be carried out.The advances in inference for data consisting of positive definite random matrices will be applied to develop new statistical theory and methods for modeling variability in biological shapes and analyzing the movement of water molecules in biological tissue. The research program benefits human development and education in the society through the training of graduate students and joint research with post-doctoral and faculty colleagues.

首席研究员（PI）将进行距离相关方法的理论和应用研究，并应用于高维天体物理数据库。这项研究将与统计学和天文学的合著者以及研究生一起完成。PI和Co-PI将开发矩阵空间上分布的汉克尔变换，并将结果应用于开发由对称正定随机矩阵组成的数据的拟合优度测试程序。PI和Co-PI将分析星系团的高维天体物理数据库，以确定多个天体物理变量之间的关联和相关性。 开展高斯分布和一般重尾分布混合分布的距离相关测度研究，利用正定随机矩阵数据推断的进展，发展新的统计理论和方法，用于生物形状变异性建模和生物组织中水分子运动分析。该研究计划通过培养研究生以及与博士后和教职员工的联合研究，使人类发展和社会教育受益。