Information Geometry

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Information Geometry

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Information Geometry

Popis výsledku anglicky

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.

Druh

B - Odborná kniha

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

978-3-319-56477-7

Počet stran knihy

407

Název nakladatele

Springer

Místo vydání

Cham

Kód UT WoS knihy

000432248800011