Simplicity and likelihood: An axiomatic approach

• 成果类型: Article
• 署名作者: Gilboa, Itzhak; Schmeidler, David
• 署名单位: Tel Aviv University; Hautes Etudes Commerciales (HEC) Paris; University System of Ohio; Ohio State University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2010.03.010
• 发表日期: 2010
• 页码: 1757-1775
• 关键词: Maximum likelihood; simplicity; model selection; Akaike Information Criterion; Minimum Description Length; axioms

摘要

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. (C) 2010 Elsevier Inc. All rights reserved.