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Simplicity and likelihood: An axiomatic approach

Author

Listed:
  • Itzhak Gilboa

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • David Schmeidler

    (TAU - Tel Aviv University)

Abstract

We suggest a model in which theories are ranked given various databases. Certain axioms on such rankings imply a numerical representation that is the sum of the log-likelihood of the theory and a fixed number for each theory, which may be interpreted as a measure of its complexity. This additive combination of log-likelihood and a measure of complexity generalizes both the Akaike Information Criterion and the Minimum Description Length criterion, which are well known in statistics and in machine learning, respectively. The axiomatic approach is suggested as a way to analyze such theory-selection criteria and judge their reasonability based on finite databases.

Suggested Citation

  • Itzhak Gilboa & David Schmeidler, 2010. "Simplicity and likelihood: An axiomatic approach," Post-Print hal-00521797, HAL.
    • Handle: RePEc:hal:journl:hal-00521797
    DOI: 10.1016/j.jet.2010.03.010
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    Cited by:

    1. , & ,, 2012. "Subjectivity in inductive inference," Theoretical Economics, Econometric Society, vol. 7(2), May.
    2. Levy, Gilat & Razin, Ronny, 2021. "A maximum likelihood approach to combining forecasts," LSE Research Online Documents on Economics 104116, London School of Economics and Political Science, LSE Library.
    3. Gilboa, Itzhak & Samuelson, Larry, 2009. "Preferring Simplicity," Foerder Institute for Economic Research Working Papers 275723, Tel-Aviv University > Foerder Institute for Economic Research.
    4. Chollete, Loran & Schmeidler, David, 2014. "Extreme Events and the Origin of Central Bank Priors," UiS Working Papers in Economics and Finance 2014/15, University of Stavanger.
    5. Gilboa, Itzhak & Wang, Fan, 2019. "Rational status quo," Journal of Economic Theory, Elsevier, vol. 181(C), pages 289-308.
    6. Chollete, Lor & Schmeidler, David, 2014. "Misspecification Aversion and Selection of Initial Priors," UiS Working Papers in Economics and Finance 2014/13, University of Stavanger.

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