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Geometric Modeling in Probability and Statistics
ISBN-13:
9783319077796
Veröffentl:
2014
Seiten:
375
Autor:
Ovidiu Calin
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors' hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields.
¿Part I: The Geometry of Statistical Models.- Statistical Models.- Explicit Examples.- Entropy on Statistical Models.- Kullback-Leibler Relative Entropy.- Informational Energy.- Maximum Entropy Distributions.- Part II: Statistical Manifolds.- An Introduction to Manifolds.- Dualistic Structure.- Dual Volume Elements.- Dual Laplacians.- Contrast Functions Geometry.-Contrast Functions on Statistical Models.- Statistical Submanifolds.- Appendix A: Information Geometry Calculator.
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