Information geometry
by Ay, Nihat
"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 te…
Read More ↓Title Statements
- Full title :Information geometry / Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer.
Summary
"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."--
Read More ↓Edition Statements
- Publication Date:©2017
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham
- Language:eng
- Publication Date:©2017
Notes
Inclou bibliografia, índex i nomenclatura.
The Physical Object
- Description:xi, 407 pàgines : : gràfics ; : 25 cm
Edition Identifiers
- ISBN:9783319564777, 3319564773
- oclc:on1055874459
Table of Contents
Introduction -- Finite information geometry -- Parametrized measure models -- The intrinsic geometry of statistical models -- Information geometry and statistics -- Fields of application of information geometry
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