How much randomness is needed for statistics?

0385834 - MÚ 2013 RIV DE eng C - Konferenční příspěvek (zahraniční konf.)
Kjos-Hanssen, B. - Taveneaux, A. - Thapen, Neil
How much randomness is needed for statistics?
How the World Computes. Berlin: Springer, 2012 - (Cooper, S.; Dawar, A.; Löwe, B.), s. 395-404. Lecture Notes in Computer Science, 7318. ISBN 978-3-642-30869-7. ISSN 0302-9743.
[CiE 2012. Turing Centerary Conference and Conference on Computability in Europe /8./. Cambridge (GB), 18.06.2012-23.06.2012]
Grant CEP: GA AV ČR IAA100190902; GA ČR GBP202/12/G061
Institucionální podpora: RVO:67985840
Klíčová slova: algorithm analysis and problem complexity * computing * symbolic and algebraic manipulation
Kód oboru RIV: BA - Obecná matematika
http://link.springer.com/chapter/10.1007/978-3-642-30870-3_40

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.
Trvalý link: http://hdl.handle.net/11104/0007491