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Information geometry

Ay, Nihat.

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Information geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Information geometry/ by Nihat Ay ... [et al.].
other author:	Ay, Nihat.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xi, 407 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Introduction -- 2 Finite information geometry -- 3 Parametrized measure models -- 4 The intrinsic geometry of statistical models -- 5 Information geometry and statistics -- 6 Application fields of information geometry -- 7 Appendix.
Contained By:	Springer eBooks
Subject:	Geometrical models in statistics. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-56478-4
ISBN:	9783319564784

Information geometry
Information geometry[electronic resource] /by Nihat Ay ... [et al.]. - Cham :Springer International Publishing :2017. - xi, 407 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics,v.640071-1136 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics ;v.64..

1 Introduction -- 2 Finite information geometry -- 3 Parametrized measure models -- 4 The intrinsic geometry of statistical models -- 5 Information geometry and statistics -- 6 Application fields of information geometry -- 7 Appendix.

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 Cramer-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.

ISBN: 9783319564784

Standard No.: 10.1007/978-3-319-56478-4doiSubjects--Topical Terms:

3252266
Geometrical models in statistics.

LC Class. No.: QA276.23

Dewey Class. No.: 519.5

Information geometry
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245 0 0 $a Information geometry $h [electronic resource] / $c by Nihat Ay ... [et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2017.
300 $a xi, 407 p. : $b ill., digital ; $c 24 cm.
490 1 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics, $x 0071-1136 ; $v v.64
505 0 $a 1 Introduction -- 2 Finite information geometry -- 3 Parametrized measure models -- 4 The intrinsic geometry of statistical models -- 5 Information geometry and statistics -- 6 Application fields of information geometry -- 7 Appendix.
520 $a 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 Cramer-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.
650 0 $a Geometrical models in statistics. $3 3252266
650 1 4 $a Statistics. $3 517247
650 2 4 $a Statistical Theory and Methods. $3 891074
650 2 4 $a Data Structures. $3 891009
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Convex and Discrete Geometry. $3 893686
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Complex Systems. $3 1566441
700 1 $a Ay, Nihat. $3 3252264
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics ; $v v.64. $3 3252265
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-56478-4
950 $a Mathematics and Statistics (Springer-11649)