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Informationen zum Autor Abhishek Bhattacharya is currently working as an assistant professor at the Indian Statistical Institute. After gaining BStat and MStat degrees from the Institute in 2002 and 2004 respectively, and a PhD from the University of Arizona in 2008, he was a postdoctoral researcher at Duke University until the end of 2010, before joining ISI in 2011. Before writing this book, he published several articles in areas as diverse as nonparametric frequentist and Bayesian statistics on non-Euclidean manifolds. All those articles can be accessed from his website. Klappentext A systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. '... this is an excellent text that will benefit many students in computer science, mathematics, and physics. However, I must stress that a proper background in differential geometry and differential calculus is needed to fully understand the material, as well as some graduate learning in advanced statistics. A significant plus of the book is the library of MATLAB codes and datasets available for download from the authors' site.' Alexander Tzanov, Computing Reviews Zusammenfassung Ideal for statisticians! this book will also interest probabilists! mathematicians! computer scientists! and morphometricians with mathematical training. It presents a systematic introduction to a general nonparametric theory of statistics on manifolds! with emphasis on manifolds of shapes. The theory has important applications in medical diagnostics! image analysis and machine vision. Inhaltsverzeichnis 1. Introduction; 2. Examples; 3. Location and spread on metric spaces; 4. Extrinsic analysis on manifolds; 5. Intrinsic analysis on manifolds; 6. Landmark-based shape spaces; 7. Kendall's similarity shape spaces ¿km; 8. The planar shape space ¿k2; 9. Reflection similarity shape spaces R¿km; 10. Stiefel manifolds; 11. Affine shape spaces A¿km; 12. Real projective spaces and projective shape spaces; 13. Nonparametric Bayes inference; 14. Regression, classification and testing; i. Differentiable manifolds; ii. Riemannian manifolds; iii. Dirichlet processes; iv. Parametric models on Sd and ¿k2; References; Subject index....
