Diffeological statistical models, the Fisher metric and probabilistic mappings

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00521519" target="_blank" >RIV/67985840:_____/20:00521519 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.3390/math8020167" target="_blank" >https://doi.org/10.3390/math8020167</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math8020167" target="_blank" >10.3390/math8020167</a>

Result language

angličtina

Original language name

Diffeological statistical models, the Fisher metric and probabilistic mappings

Original language description

We introduce the notion of a C^k -diffeological statistical model, which allows us to apply the theory of diffeological spaces to (possibly singular) statistical models. In particular, we introduce a class of almost 2-integrable C^k -diffeological statistical models that encompasses all known statistical models for which the Fisher metric is defined. This class contains a statistical model which does not appear in the Ay–Jost–Lê–Schwachhöfer theory of parametrized measure models. Then, we show that, for any positive integer k , the class of almost 2-integrable C^k -diffeological statistical models is preserved under probabilistic mappings. Furthermore, the monotonicity Theorem for the Fisher metric also holds for this class. As a consequence, the Fisher metric on an almost 2-integrable C^k -diffeological statistical model P⊂P(X) is preserved under any probabilistic mapping T:X⇝Y that is sufficient w.r.t. P. Finally, we extend the Cramér–Rao inequality to the class of 2-integrable C^k -diffeological statistical models.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GC18-01953J" target="_blank" >GC18-01953J: Geometric methods in statistical learning theory and applications</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

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

Name of the periodical

Mathematics

ISSN

2227-7390

e-ISSN

—

Volume of the periodical

8

Issue of the periodical within the volume

2

Country of publishing house

CH - SWITZERLAND

Number of pages

13

Pages from-to

167

UT code for WoS article

000519234000022

EID of the result in the Scopus database

2-s2.0-85080125263