Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) Authors: Nihat Ay - Jürgen Jost - Hông Vân Lê - Lorenz Schwachhöfer ISBN-10: 3319564773 ISBN-13: 9783319564777 Edition: 1st ed. 2017 Released: 2017-08-26 Hardcover: 407 pages List Price Book Description 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. Table of contents Chapter 1: Introduction Chapter 2: Finite Information Geometry Chapter 3: Parametrized Measure Models Chapter 4: The Intrinsic Geometry of Statistical Models Chapter 5: Information Geometry and Statistics Chapter 6: Fields of Application of Information Geometry Appendix A: Measure Theory Appendix B: Riemannian Geometry Appendix C: Banach Manifolds 预览－Springer Information Geometry 3319564773.pdf 资源下载资源下载价格10元立即购买 1111 未经允许不得转载：电子书百科大全 » Information Geometry
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