Information Geometry
Ay, Nihat, Jost, Jürgen, Lê, Hông Vân, Schwachhöfer, Lorenz
Produktnummer:
18a0a564c44ace4ce7916d2f4b8014d010
Autor: | Ay, Nihat Jost, Jürgen Lê, Hông Vân Schwachhöfer, Lorenz |
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Themengebiete: | 53B05, 46B20, 94A15, 94A17, 94B27 60A10, 62B05, 62B10, 62G05, 53B21 Alpha Connections Amari-Chentsov Tensor Divergences Fisher Metric Information Geometry data structures |
Veröffentlichungsdatum: | 02.10.2017 |
EAN: | 9783319564777 |
Sprache: | Englisch |
Seitenzahl: | 407 |
Produktart: | Gebunden |
Verlag: | Springer International Publishing |
Produktinformationen "Information Geometry"
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.

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