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Lieferstatus:	i.d.R. innert 7-14 Tagen versandfertig
Veröffentlichung:	August 2018
Genre:	Schulbücher
	Algebraic Geometry / Algorithms & data structures / Applied mathematics / B / Complex systems / Convex and Discrete Geometry / Convex geometry / Data Structures / Data structures (Computer science) / Data Structures and Information Theory / Differential & Riemannian geometry / Differential Geometry / Discrete geometry / Discrete Mathematics / Functional Analysis / Functional analysis & transforms / Mathematics and Statistics / Statistical Theory and Methods / Statistics / System Theory mehr...
ISBN:	9783319859217
EAN-Code:	9783319859217
Verlag:	Springer EN
Einband:	Kartoniert
Sprache:	English
Serie:	#64 - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Dimensionen:	H 235 mm / B 155 mm / D
Gewicht:	640 gr
Seiten:	418
Illustration:	XI, 407 p. 15 illus., schwarz-weiss Illustrationen
Zus. Info:	EUDR exemption - product or manufacturing materials placed on the market prior to 31.12.2025.
Bewertung:	Titel bewerten / Meinung schreiben

Inhalt:

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.