Information Geometry

Nonfiction, Computers, Advanced Computing, Programming, Data Modeling & Design, Science & Nature, Mathematics, Statistics
Cover of the book Information Geometry by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer ISBN: 9783319564784
Publisher: Springer International Publishing Publication: August 25, 2017
Imprint: Springer Language: English
Author: Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
ISBN: 9783319564784
Publisher: Springer International Publishing
Publication: August 25, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Advancing Interdisciplinary Approaches to International Relations by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Modern Piezoelectric Energy-Harvesting Materials by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book The 8th International Conference on Computer Engineering and Networks (CENet2018) by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Surgery of Conotruncal Anomalies by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Advanced Hybrid Information Processing by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Climate Change in Cyprus by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Automation, Communication and Cybernetics in Science and Engineering 2015/2016 by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Mathematical Advances Towards Sustainable Environmental Systems by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Post-Quantum Cryptography by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book The Lysenko Controversy as a Global Phenomenon, Volume 2 by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book The Complete Business Guide for a Successful Medical Practice by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book New Techniques in Foot and Ankle Surgery by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Online Citizen Science and the Widening of Academia by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Robust Simulation for Mega-Risks by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
Cover of the book Emerging Contaminants in River Ecosystems by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy