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Simplicity and Likelihood: An Axiomatic Approach

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  • Itzhak Gilboa
  • David Schmeidler

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.
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Suggested Citation

  • Itzhak Gilboa & David Schmeidler, 2008. "Simplicity and Likelihood: An Axiomatic Approach," Levine's Working Paper Archive 122247000000001970, David K. Levine.
    • Handle: RePEc:cla:levarc:122247000000001970
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    References listed on IDEAS

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    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. , & ,, 2012. "Subjectivity in inductive inference," Theoretical Economics, Econometric Society, vol. 7(2), May.
    3. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2012. "Probabilities as Similarity-Weighted Frequencies," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 7, pages 169-184, World Scientific Publishing Co. Pte. Ltd..
    4. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, September.
    5. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2012. "Empirical Similarity," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 9, pages 211-243, World Scientific Publishing Co. Pte. Ltd..
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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. 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.
    4. Gilboa, Itzhak & Wang, Fan, 2019. "Rational status quo," Journal of Economic Theory, Elsevier, vol. 181(C), pages 289-308.
    5. Chollete, Lor & Schmeidler, David, 2014. "Misspecification Aversion and Selection of Initial Priors," UiS Working Papers in Economics and Finance 2014/13, University of Stavanger.
    6. Gilboa, Itzhak & Samuelson, Larry, 2009. "Preferring Simplicity," Foerder Institute for Economic Research Working Papers 275723, Tel-Aviv University > Foerder Institute for Economic Research.

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