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Inverting Bernoulli’s Theorem: The Original Sin

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Author Info
Xavier De Scheemaekere () (Centre Emile Bernheim, Solvay Brussels School of Economics and Management, Université Libre de Bruxelles, Brussels.)
Ariane Szafarz () (Centre Emile Bernheim, Solvay Brussels School of Economics and Management, Université Libre de Bruxelles, Brussels and DULBEA, Université Libre de Bruxelles)

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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: http://www.solvay.edu/EN/Research/Bernheim/documents/wp08029.pdf
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File Function: First version, 2008
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Publisher Info
Paper provided by Université Libre de Bruxelles, Solvay Brussels School of Economics and Management, Centre Emile Bernheim (CEB) in its series Working Papers CEB with number 08-029.RS.

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Length: 26 pages
Date of creation: Oct 2008
Date of revision:
Handle: RePEc:sol:wpaper:08-029

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

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Find related papers by JEL classification:
N01 - Economic History - - General - - - Development of the Discipline: Historiographical; Sources and Methods
B31 - Schools of Economic Thought and Methodology - - History of Thought: Individuals - - - Individuals
C65 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Miscellaneous Mathematical Tools

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