Empirical interpretation of imprecise probabilities

Cattaneo, Marco

Abstract

This paper investigates the possibility of a frequentist interpretation of imprecise probabilities, by generalizing the approach of Bernoulli’s Ars Conjectandi. That is, by studying, in the case of games of chance, under which assumptions imprecise probabilities can be satisfactorily estimated from data. In fact, estimability on the basis of finite amounts of data is a necessary condition for imprecise probabilities in order to have a clear empirical meaning. Unfortunately, imprecise probabilities can be estimated arbitrarily well from data only in very limited settings.

Citation

Cattaneo, M. (2017). Empirical interpretation of imprecise probabilities. Proceedings of Machine Learning Research, 62, 61-72

• Journal Article Type: Article
• Acceptance Date: Apr 14, 2017
• Publication Date: 2017-07
• Deposit Date: Jul 7, 2017
• Publicly Available Date: Jul 31, 2017
• Journal: Proceedings of machine learning research
• Print ISSN: 2640-3498
• Electronic ISSN: 1938-7228
• Peer Reviewed: Peer Reviewed
• Volume: 62
• Pages: 61-72
• Keywords: Imprecise probabilities, Frequentist interpretation, Empirical meaning, Bag of marbles, Strong estimability, Consistent estimators, Empirical recognizability
• Public URL: https://hull-repository.worktribe.com/output/453373
• Publisher URL: http://proceedings.mlr.press/v62/cattaneo17a.html
• Additional Information: This is a copy of a paper published in Proceedings of machine learning research, 2017, v.62.