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How much randomness is needed for statistics?
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SYSNO ASEP 0385834 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title How much randomness is needed for statistics? Author(s) Kjos-Hanssen, B. (US)
Taveneaux, A. (FR)
Thapen, Neil (MU-W) RID, SAISource Title How the World Computes. - Berlin : Springer, 2012 / Cooper S.B. ; Dawar A. ; Löwe B. - ISSN 0302-9743 - ISBN 978-3-642-30869-7 Pages s. 395-404 Number of pages 10 s. Publication form Print - P Action CiE 2012. Turing Centerary Conference and Conference on Computability in Europe /8./ Event date 18.06.2012-23.06.2012 VEvent location Cambridge Country GB - United Kingdom Event type WRD Language eng - English Country DE - Germany Keywords algorithm analysis and problem complexity ; computing ; symbolic and algebraic manipulation Subject RIV BA - General Mathematics R&D Projects IAA100190902 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) GBP202/12/G061 GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 EID SCOPUS 84862198297 DOI 10.1007/978-3-642-30870-3_40 Annotation In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure λ, a choice needs to be made. One approach is to allow randomness tests to access the measure λ 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 λ (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-Löf randomness and the measure λ 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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