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Simplicity and likelihood: An axiomatic approach

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  • Gilboa, Itzhak
  • Schmeidler, David

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 5 (September)
Pages: 1757-1775

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:1757-1775

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Maximum likelihood Simplicity Model selection Akaike Information Criterion Minimum Description Length Axioms;

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  1. Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," NajEcon Working Paper Reviews 391749000000000544, www.najecon.org.
  2. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, 07.
  3. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
  4. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
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