Information geometry

    • Jost, Jürgen
    • Lê, Hông Vân
    • Schwachhöfer, Lorenz

著者

    • Jost, Jürgen
    • Lê, Hông Vân
    • Schwachhöfer, Lorenz

書誌事項

Information geometry

Nihat Ay ... [et al.]

(Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge . A series of modern surveys in mathematics ; v. 64)

Springer, c2017

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注記

Other authors: Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer

Includes bibliographical references (p. 387-396) and index

内容説明・目次

内容説明

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.

目次

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.

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詳細情報

  • NII書誌ID(NCID)
    BB24632393
  • ISBN
    • 9783319564777
  • LCCN
    2017951855
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cham
  • ページ数/冊数
    xi, 407 p.
  • 大きさ
    25 cm
  • 親書誌ID
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