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

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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.