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Ay, Nihat, Jost, Jürgen, Lê, Hông Vân - Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) - 9783319564777 - V9783319564777
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Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)

€ 187.19
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Description for Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) Hardcover. Series: Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematics. Num Pages: biography. BIC Classification: PBKF; PBMP; PBMW; PBW; UMB. Category: (P) Professional & Vocational. Dimension: 235 x 155. .

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.  ... Read more

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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Product Details

Format
Hardback
Publication date
2017
Publisher
Springer
Condition
New
Series
Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of Modern Surveys in Mathematic
Number of Pages
407
Place of Publication
Cham, Switzerland
ISBN
9783319564777
SKU
V9783319564777
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15

About Ay, Nihat, Jost, Jürgen, Lê, Hông Vân
Nihat Ay studied mathematics and physics at the Ruhr University Bochum and received his Ph.D. in mathematics from the University of Leipzig in 2001. He was a Postdoc at the Santa Fe Institute and at the Redwood Center for Theoretical Neuroscience, UC Berkeley.  Since 2005, he has been group leader at the Max Planck Institute for Mathematics in the Sciences ... Read more

Reviews for Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
“The monograph is very timely and welcome. It will become a standard textbook and reference for the field. It is not only accessible and useful for scientists who work in probability or statistics, but also for all graduate students of mathematics.” (Andreas Knauf, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 121, 2019) “This book also provides a general framework that integrates the ... Read more

Goodreads reviews for Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)


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