Information Geometry

• Main Authors: Ay, Nihat (Author), Jost, Jürgen (Author), Lê, Hông Vân (Author), Schwachhöfer, Lorenz (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 64
• Subjects: Statistics.; Data structures (Computer science).; Functional analysis.; System theory.; Convex geometry.; Discrete geometry.; Differential geometry.; Statistical Theory and Methods.; Data Structures.; Differential Geometry.; Convex and Discrete Geometry.; Functional Analysis.; Complex Systems.

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 geometr...

Table of Contents:

• 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.