Information Geometry

0477908 - MÚ 2018 RIV CH eng B - Monography
Ay, N. - Jost, J. - Le, Hong-Van - Schwachhöfer, L.
Information Geometry.
1. - Cham: Springer, 2017. 407 s. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Volume 64. ISBN 978-3-319-56477-7. ISSN 0071-1136
Institutional support: RVO:67985840
Keywords : information geometry * Fisher metric * Amari-Chentsov tensor
OECD category: Pure mathematics
https://link.springer.com/book/10.1007/978-3-319-56478-4

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.
Permanent Link: http://hdl.handle.net/11104/0274110