TY - JOUR

T1 - Simplicity and likelihood

T2 - An axiomatic approach

AU - Gilboa, Itzhak

AU - Schmeidler, David

N1 - Funding Information:
✩ We thank Yoav Binyamini, Offer Lieberman, two anonymous referees and the associate editor for comments and suggestions. This project was supported by the Pinhas Sapir Center for Development and Israel Science Foundation Grant Nos. 975/03 and 355/06. * Corresponding author at: Tel-Aviv University, Israel. E-mail addresses: tzachigilboa@gmail.com (I. Gilboa), schmeid@tau.ac.il (D. Schmeidler).

PY - 2010/9

Y1 - 2010/9

N2 - 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.

AB - 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.

KW - Akaike Information Criterion

KW - Axioms

KW - Maximum likelihood

KW - Minimum Description Length

KW - Model selection

KW - Simplicity

UR - http://www.scopus.com/inward/record.url?scp=77955922930&partnerID=8YFLogxK

U2 - 10.1016/j.jet.2010.03.010

DO - 10.1016/j.jet.2010.03.010

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AN - SCOPUS:77955922930

SN - 0022-0531

VL - 145

SP - 1757

EP - 1775

JO - Journal of Economic Theory

JF - Journal of Economic Theory

IS - 5

ER -