Simplicity and likelihood: An axiomatic approach

Itzhak Gilboa and David Schmeidler

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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.

Keywords: Maximum likelihood; Simplicity; Model selection; Akaike Information Criterion; Minimum Description Length; Axioms (search for similar items in EconPapers)
Date: 2010-09
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Citations: View citations in EconPapers (4)

Published in Journal of Economic Theory, 2010, 145 (5), pp.1757-1775. ⟨10.1016/j.jet.2010.03.010⟩

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Journal Article: Simplicity and likelihood: An axiomatic approach (2010)
Working Paper: Simplicity and Likelihood: An Axiomatic Approach (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00521797

DOI: 10.1016/j.jet.2010.03.010

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