Information Geometry PDF
By:Nihat Ay,Jürgen Jost,Hông Vân Lê,Lorenz Schwachhöfer
Published on 2017-08-25 by Springer
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
This Book was ranked at 29 by Google Books for keyword Santé.
Book ID of Information Geometry's Books is pLsyDwAAQBAJ, Book which was written byNihat Ay,Jürgen Jost,Hông Vân Lê,Lorenz Schwachhöferhave ETAG "YuPLqeiKTJs"
Book which was published by Springer since 2017-08-25 have ISBNs, ISBN 13 Code is 9783319564784 and ISBN 10 Code is 3319564781
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Book which have "407 Pages" is Printed at BOOK under CategoryMathematics
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