IDEAS home Printed from https://ideas.repec.org/p/sol/wpaper/2013-77259.html
   My bibliography  Save this paper

The Inference Fallacy From Bernoulli to Kolmogorov

Author

Listed:
  • Xavier De Scheemaekere
  • Ariane Szafarz

Abstract

Bernoulli’s (1713) well-known Law of Large Numbers (LLN) establishes a legitimate one-way transition from mathematical probability to observed frequency. However, Bernoulli went one step further and abusively introduced the inverse proposition. Based on a careful analysis of Bernoulli’s original proof, this paper identifies this appealing, but illegitimate, inversion of LLN as a strong driver of confusion among probabilists. Indeed, during more than two centuries this “inference fallacy” hampered the emergence of rigorous mathematical foundations for the theory of probability. In particular, the confusion pertaining to the status of statistical inference was detrimental to both Laplace’s approach based on “equipossibility” and Mises’ approach based on “collectives”. Only Kolmogorov’s (1933) axiomatization made it possible to adequately frame statistical inference within probability theory. This paper argues that a key factor in Kolmogorov’s success has been his ability to overcome the inference fallacy.

Suggested Citation

  • Xavier De Scheemaekere & Ariane Szafarz, 2011. "The Inference Fallacy From Bernoulli to Kolmogorov," Working Papers CEB 11-006, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:sol:wpaper:2013/77259
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/77259/4/wp11006.pdf
    File Function: wp11006
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xavier De Scheemaekere & Kim Oosterlinck & Ariane Szafarz, 2012. "Addressing Economic Crises: The Reference-Class Problem," Working Papers CEB 12-024, ULB -- Universite Libre de Bruxelles.
    2. Xavier De Scheemaekere & Kim Oosterlinck & Ariane Szafarz, 2014. "Issues in Identifying Economic Crises: Insights from History," Working Papers CEB 14-014, ULB -- Universite Libre de Bruxelles.
    3. Xavier De Scheemaekere & Ariane Szafarz, 2008. "Inverting Bernoulli's theorem: the original sin," Working Papers CEB 08-029.RS, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

    Probability; Bernoulli; Kolmogorov; Statistics; Law of Large Numbers;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sol:wpaper:2013/77259. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/cebulbe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.