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＜電子ブック＞
Information Geometry / by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 64)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	XI, 407 p. 15 illus : online resource
著者標目	*Ay, Nihat author Jost, Jürgen author Lê, Hông Vân author Schwachhöfer, Lorenz author SpringerLink (Online service)
件　名	LCSH:Statistics  LCSH:Artificial intelligence -- Data processing  全ての件名で検索 LCSH:Geometry, Differential LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Functional analysis LCSH:System theory FREE:Statistical Theory and Methods FREE:Data Science FREE:Differential Geometry FREE:Convex and Discrete Geometry FREE:Functional Analysis FREE:Complex Systems
一般注記	1 Introduction -- 2 Finite information geometry -- 3 Parametrized measure models -- 4 The intrinsic geometry of statistical models -- 5 Information geometry and statistics -- 6 Application fields of information geometry -- 7 Appendix 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 HTTP:URL=https://doi.org/10.1007/978-3-319-56478-4

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