國立虎尾科技大學 |

Information geometry

Record Type:	Language materials, printed : 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.;
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.65..

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:

1200309
Geometrical models in statistics.

LC Class. No.: QA276.23

Dewey Class. No.: 519.5

Information geometry
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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.
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650 1 4 $a Statistics. $3 556824
650 2 4 $a Statistical Theory and Methods. $3 671396
650 2 4 $a Data Structures. $3 669824
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Convex and Discrete Geometry. $3 672138
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Complex Systems. $3 888664
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