How much randomness is needed for statistics?

0430391 - MÚ 2015 RIV NL eng J - Článek v odborném periodiku
Kjos-Hanssen, B. - Taveneaux, A. - Thapen, Neil
How much randomness is needed for statistics?
Annals of Pure and Applied Logic. Roč. 165, č. 9 (2014), s. 1470-1483. ISSN 0168-0072. E-ISSN 1873-2461
Grant CEP: GA AV ČR IAA100190902; GA ČR GBP202/12/G061
Institucionální podpora: RVO:67985840
Klíčová slova: hippocratic randomness * Martigales * Bernoulli measures
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.548, rok: 2014
http://www.sciencedirect.com/science/article/pii/S0168007214000451

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, classical randomness 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.
Trvalý link: http://hdl.handle.net/11104/0235337