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OverviewThis 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. Full Product DetailsAuthor: Ovidiu Calin , Constantin UdriştePublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: Softcover reprint of the original 1st ed. 2014 Weight: 6.757kg ISBN: 9783319381626ISBN 10: 3319381628 Pages: 375 Publication Date: 30 April 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPart 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.ReviewsThe 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) 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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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