Authors:
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: sn.pub/extras
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Table of contents (13 chapters)
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Front Matter
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The Geometry of Statistical Models
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Front Matter
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Back Matter
About this book
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.
Reviews
“The book under review presents a concise introduction to the mathematical foundation of information geometry and contains an overview of other related areas of interest and applications. … This book is well-written and will be a useful and important addition to the resources of practitioners and many others engaged in probability theory, mathematical statistics and related subjects. I recommend it highly as a textbook for a course directed at graduate or advanced undergraduate students.” (Prasanna Sahoo, zbMATH, Vol. 1325.60001, 2016)
Authors and Affiliations
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Department of Mathematics, Eastern Michigan University, Ypsilanti, USA
Ovidiu Calin
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Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Bucharest, Romania
Constantin Udrişte
Bibliographic Information
Book Title: Geometric Modeling in Probability and Statistics
Authors: Ovidiu Calin, Constantin Udrişte
DOI: https://doi.org/10.1007/978-3-319-07779-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-07778-9Published: 01 August 2014
Softcover ISBN: 978-3-319-38162-6Published: 30 April 2017
eBook ISBN: 978-3-319-07779-6Published: 17 July 2014
Edition Number: 1
Number of Pages: XXIII, 375
Number of Illustrations: 19 b/w illustrations, 3 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Geometry, Statistical Theory and Methods