Simplicity and Likelihood: An axiomatic approach

I. GILBOA, D. Schmeidler

Journal of Economic Theory

September 2010, vol. 145, n°5, pp.1757-1775

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

Accepté le 19 février 2010We 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. © 2010 Elsevier Inc. All rights reserved.Author Keywords Akaike Information Criterion; Axioms; Maximum likelihood; Minimum Description Length; Model selection; Simplicity