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Inverting Bernoulli's theorem: the original sin

Author

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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.

Suggested Citation

  • Xavier De Scheemaekere & Ariane Szafarz, 2008. "Inverting Bernoulli's theorem: the original sin," Working Papers CEB 08-029.RS, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:sol:wpaper:08-029
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    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/14571/1/rou-0194.pdf
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    References listed on IDEAS

    as
    1. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    2. Xavier De Scheemaekere & Ariane Szafarz, 2008. "The special status of mathematical probability: a historical sketch," Working Papers CEB 08-017.RS, ULB -- Universite Libre de Bruxelles.
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    More about this item

    Keywords

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

    JEL classification:

    • N01 - Economic History - - General - - - Development of the Discipline: Historiographical; Sources and Methods
    • B31 - Schools of Economic Thought and Methodology - - History of Economic Thought: Individuals - - - Individuals
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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