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How Much Randomness Is Needed for Statistics?

  • Bjørn Kjos-Hanssen
  • Antoine Taveneaux
  • Neil Thapen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)

Abstract

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.

Keywords

Steklov Institute Random Sequence Bernoulli Trial Randomness Test Binary Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bjørn Kjos-Hanssen
    • 1
  • Antoine Taveneaux
    • 2
  • Neil Thapen
    • 3
    • 4
  1. 1.University of Hawai‘i at MānoaHonoluluUnited States of America
  2. 2.Laboratoire d’Informatique Algorithmique: Fondements et Applications (LIAFA)Université Paris Diderot-Paris 7Paris Cedex 13France
  3. 3.Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  4. 4.Isaac Newton Institute for Mathematical SciencesCambridgeUnited Kingdom

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