On the concept of Bernoulliness

Vladimir Vovk

On the concept of Bernoulliness

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arxiv 1612.08859 v1 pith:BXOBX272 submitted 2016-12-28 math.ST stat.TH

Vladimir Vovk This is my paper · ORCID

classification math.STstat.TH

keywords definitionfinitegivessequenceanotherappendixbackgroundbernoulli

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The first part of this paper is another English translation of a 1986 note. It gives a natural definition of a finite Bernoulli sequence (i.e., a typical realization of a finite sequence of binary IID trials) and compares it with the Kolmogorov--Martin-Lof definition, which is interpreted as defining exchangeable sequences. The appendix gives the historical background and proofs.

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In classification, every confidence predictor that is valid under IID data can be transformed into a conformal predictor with an explicit, constant-free bound on the loss of efficiency.

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