Inverting Bernoulli's theorem: the original sin
AbstractThis 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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Bibliographic InfoPaper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers CEB with number 08-029.RS.
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)
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More information through EDIRC
Probability; Bernoulli’s Theorem; Mathematics; Statistics.;
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 Economic Thought: Individuals - - - Individuals
- C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-10-13 (All new papers)
- NEP-ECM-2008-10-13 (Econometrics)
- NEP-HIS-2008-10-13 (Business, Economic & Financial History)
- NEP-HPE-2008-10-13 (History & Philosophy of Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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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