How much randomness is needed for statistics?

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00430391" target="_blank" >RIV/67985840:_____/14:00430391 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.apal.2014.04.014" target="_blank" >http://dx.doi.org/10.1016/j.apal.2014.04.014</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apal.2014.04.014" target="_blank" >10.1016/j.apal.2014.04.014</a>

Jazyk výsledku

angličtina

Název v původním jazyce

How much randomness is needed for statistics?

Popis výsledku v původním jazyce

In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure lambda, a choice needs to be made. One approach is to allow randomness tests to access the measure lambda as an oracle (which we call the"classical approach"). The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the information contained in lambda (we call this approach "Hippocratic"). While the Hippocratic approach is in general much more restrictive, there are cases where the two coincide. The first author showed in 2010 that in the particular case where the notion of randomness considered is Martin-Lof randomness and the measure lambda is a Bernoulli measure, classicalrandomness and Hippocratic randomness coincide. In this paper, we prove that this result no longer holds for other notions of randomness, namely computable randomness and stochasticity.

Název v anglickém jazyce

How much randomness is needed for statistics?

Popis výsledku anglicky

In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure lambda, a choice needs to be made. One approach is to allow randomness tests to access the measure lambda as an oracle (which we call the"classical approach"). The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the information contained in lambda (we call this approach "Hippocratic"). While the Hippocratic approach is in general much more restrictive, there are cases where the two coincide. The first author showed in 2010 that in the particular case where the notion of randomness considered is Martin-Lof randomness and the measure lambda is a Bernoulli measure, classicalrandomness and Hippocratic randomness coincide. In this paper, we prove that this result no longer holds for other notions of randomness, namely computable randomness and stochasticity.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Annals of Pure and Applied Logic

ISSN

0168-0072

e-ISSN

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Svazek periodika

165

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

1470-1483

Kód UT WoS článku

000337869300008

EID výsledku v databázi Scopus

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