Parametrized measure models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00486135" target="_blank" >RIV/67985840:_____/18:00486135 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.3150/16-BEJ910" target="_blank" >http://dx.doi.org/10.3150/16-BEJ910</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3150/16-BEJ910" target="_blank" >10.3150/16-BEJ910</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parametrized measure models

Popis výsledku v původním jazyce

We develop a new and general notion of parametric measure models and statistical models on an arbitrary sample space Omega which does not assume that all measures of the model have the same null sets. This is given by a differentiable map from the parameter manifold M into the set of finite measures or probability measures on Omega, respectively, which is differentiable when regarded as a map into the Banach space of all signed measures on Omega. Furthermore, we also give a rigorous definition of roots of measures and give a natural characterization of the Fisher metric and the Amari-Chentsov tensor as the pullback of tensors defined on the space of roots of measures. We show that many features such as the preservation of this tensor under sufficient statistics and the monotonicity formula hold even in this very general set-up.

Název v anglickém jazyce

Parametrized measure models

Popis výsledku anglicky

We develop a new and general notion of parametric measure models and statistical models on an arbitrary sample space Omega which does not assume that all measures of the model have the same null sets. This is given by a differentiable map from the parameter manifold M into the set of finite measures or probability measures on Omega, respectively, which is differentiable when regarded as a map into the Banach space of all signed measures on Omega. Furthermore, we also give a rigorous definition of roots of measures and give a natural characterization of the Fisher metric and the Amari-Chentsov tensor as the pullback of tensors defined on the space of roots of measures. We show that many features such as the preservation of this tensor under sufficient statistics and the monotonicity formula hold even in this very general set-up.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Bernoulli

ISSN

1350-7265

e-ISSN

—

Svazek periodika

24

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

34

Strana od-do

1692-1725

Kód UT WoS článku

000426274800004

EID výsledku v databázi Scopus

2-s2.0-85041905331