Geometric Modeling in Probability and Stat...

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Sprache: Englisch

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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.
This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Über den Autor

Ovidiu Calin, a graduate from University of Toronto, is a professor at Eastern Michigan University and a former visiting professor at Princeton University and University of Notre Dame. He has delivered numerous lectures at several universities in Japan, Hong Kong, Taiwan, and Kuwait over the last 15 years. His publications include over 60 articles and 8 books in the fields of machine learning, computational finance, stochastic processes, variational calculus and geometric analysis.

Zusammenfassung

Comprehensive treatment of probability theory from the framework of differential geometry

Well-chosen problems covering a diverse spectrum of topics

Use of hands-on software to clarify and understand informational geometry concepts

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2017
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxiii 375 S. 19 s/w Illustr. 3 farbige Illustr. 375 p. 22 illus. 3 illus. in color.
ISBN-13:	9783319381626
ISBN-10:	3319381628
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Calin, Ovidiu Udri¿te, Constantin
Auflage:	Softcover reprint of the original 1st edition 2014
Hersteller:	Springer Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 21 mm
Von/Mit:	Ovidiu Calin (u. a.)
Erscheinungsdatum:	30.04.2017
Gewicht:	0,677 kg