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arXiv · 0806.4484

On empirical meaning of randomness with respect to a real parameter

Vladimir V'yugin
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Abstract

We study the empirical meaning of randomness with respect to a family of probability distributions $P_θ$, where $θ$ is a real parameter, using algorithmic randomness theory. In the case when for a computable probability distribution $P_θ$ an effectively strongly consistent estimate exists, we show that the Levin's a priory semicomputable semimeasure of the set of all $P_θ$-random sequences is positive if and only if the parameter $θ$ is a computable real number. The different methods for generating ``meaningful'' $P_θ$-random sequences with noncomputable $θ$ are discussed.

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Vladimir V'yugin. 2009-06-25. On empirical meaning of randomness with respect to a real parameter. https://arxiv.org/abs/0806.4484

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