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

首席研究员（PI）将对距离相关方法进行理论和应用研究，并将其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共同作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Hankel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。对高斯分布与一般重尾分布混合的距离相关测度进行了研究。在由正定随机矩阵组成的数据推理方面的进展将应用于发展新的统计理论和方法，以模拟生物形状的变异性和分析生物组织中水分子的运动。该研究项目通过培养研究生和与博士后和教职员工的联合研究，促进社会的人类发展和教育。

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.