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Inverting Bernoulli's theorem: the original sin

Xavier De Scheemaekere () and Ariane Szafarz

No 08-029.RS, Working Papers CEB from ULB -- Universite Libre de Bruxelles

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.

Keywords: Probability; Bernoulli’s Theorem; Mathematics; Statistics. (search for similar items in EconPapers)
JEL-codes: N01 B31 C65 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-his and nep-hpe
Date: 2008-10
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Published by: Université Libre de Bruxelles, Solvay Business School, Centre Emile Bernheim (CEB)

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