Information Geometry

  • Nihat Ay
  • Jürgen Jost
  • Hông Vân Lê
  • Lorenz Schwachhöfer

Table of contents

  1. Front Matter
    Pages I-XI
  2. Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
    Pages 1-23
  3. Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
    Pages 25-119
  4. Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
    Pages 121-184
  5. Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
    Pages 185-239
  6. Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
    Pages 241-293
  7. Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
    Pages 295-360
  8. Back Matter
    Pages 361-407

About this book

Introduction

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.

Keywords

60A10, 62B05, 62B10, 62G05, 53B21 53B05, 46B20, 94A15, 94A17, 94B27 Information Geometry Fisher Metric Amari-Chentsov Tensor Alpha Connections Divergences

Authors and affiliations

  • Nihat Ay
    • 1
  • Jürgen Jost
    • 2
  • Hông Vân Lê
    • 3
  • Lorenz Schwachhöfer
    • 4
  1. 1.Research Group AyMPI für Mathematik in den NaturwissenschaftenLeipzigGermany
  2. 2.Geometrische MethodenMPI für Mathematik in den NaturwissenschaftenLeipzigGermany
  3. 3.Mathematical Institute of ASCRCzech Academy of SciencesPraha 1Czech Republic
  4. 4.Fakultät für MathematikUniversität DortmundDortmundGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-56478-4
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-56477-7
  • Online ISBN 978-3-319-56478-4
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • About this book