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Simplicity and likelihood: An axiomatic approach

  • Gilboa, Itzhak
  • Schmeidler, David

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. repec:cup:cbooks:9780521802345 is not listed on IDEAS
  2. Itzhak Gilboa & David Schmeidler, 2001. "Inductive Inference: An Axiomatic Approach," Cowles Foundation Discussion Papers 1339, Cowles Foundation for Research in Economics, Yale University.
  3. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Probabilities as Similarity-Weighted Frequencies," Levine's Bibliography 122247000000000696, UCLA Department of Economics.
  4. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Levine's Bibliography 122247000000000684, UCLA Department of Economics.
  5. repec:cup:cbooks:9780521003117 is not listed on IDEAS
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