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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
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 -