| Dewey Class |
519.5 |
| Title |
Information Geometry ([EBook]) / by Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer. |
| Author |
Ay, Nihat |
| Added Personal Name |
Jost, Jürgen , 1956- author. |
| Vân Lê, Hông |
| Schwachhöfer, Lorenz |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Cham : Springer International Publishing , 2017. |
| Physical Details |
: online resource. |
| Series |
Ergebnisse der Mathematik und ihrer Grenzgebiete; 3. Folge 0071-1136 ; ; 64 |
| ISBN |
9783319564784 |
| Summary Note |
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 Cram?-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.: |
| Contents note |
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. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-3-319-56478-4 |
| See Also |
http://dx.doi.org/10.1007/978-3-319-56478-4 |
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