Information Geometry

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00477908" target="_blank" >RIV/67985840:_____/17:00477908 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-56478-4" target="_blank" >http://dx.doi.org/10.1007/978-3-319-56478-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-56478-4" target="_blank" >10.1007/978-3-319-56478-4</a>

Result language
angličtina
Original language name
Information Geometry
Original language description
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.nThis 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.
Czech name
—
Czech description
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)