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Inverting Bernoulli's theorem: the original sin

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  • Xavier De Scheemaekere
  • Ariane Szafarz

Abstract

This paper sheds a new light on the gap between a priori and a posteriori probabilities by concentrating on the evolution of the mathematical concept. It identifies the illegitimate use of Bernoulli’s law of large numbers as the probabilists’ original sin. The resulting confusion on the mathematical foundation for statistical inference was detrimental to Laplace’s definition of probability in terms of equi-possible outcomes as well as to von Mises’ frequentist approach. On the opposite, Kolmogorov’s analytical axiomatization of probability theory enables a priori and a posteriori probabilities to relate to each other without contradiction, allowing a consistent mathematical specification of the dual nature of probability. Therefore, only in Kolmorogorov’s formalism is statistical inference rigorously framed.

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File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/14571/1/rou-0194.pdf
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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers CEB with number 08-029.RS.

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Length: 26 p.
Date of creation: Oct 2008
Date of revision:
Publication status: Published by: Université Libre de Bruxelles, Solvay Business School, Centre Emile Bernheim (CEB)
Handle: RePEc:sol:wpaper:08-029

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Keywords: Probability; Bernoulli’s Theorem; Mathematics; Statistics.;

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  1. Xavier De Scheemaekere & Ariane Szafarz, 2009. "The Special Status of Mathematical Probability: A Historical Sketch," ULB Institutional Repository 2013/95543, ULB -- Universite Libre de Bruxelles.
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