Simplicity and likelihood: An axiomatic approach

Itzhak Gilboa (1) , David Schmeidler (2)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 TAU - Tel Aviv University

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.

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

Domaines: Economie et sciences de la décision

Itzhak Gilboa, David Schmeidler. Simplicity and likelihood: An axiomatic approach. Journal of Economic Theory, 2010, 145 (5), pp.1757-1775. ⟨10.1016/j.jet.2010.03.010⟩. ⟨hal-00521797⟩