A Novel Bayes’ Theorem for Upper Probabilities

Caprio, Michele; Sale, Yusuf; Hüllermeier, Eyke und Lee, Insup (4. August 2023): A Novel Bayes’ Theorem for Upper Probabilities. Epi UAI 2023 - First International Workshop on Epistemic Uncertainty in Artificial Intelligence, Pittsburgh, PA, USA, August 4, 2023. In: Epistemic Uncertainty in Artificial Intelligence, Bd. 14523 S. 1-12

Abstract

In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes’ posterior probability of a measurable set A, when the prior lies in a class of probability measures and the likelihood is precise. They also give a sufficient condition for such upper bound to hold with equality. In this paper, we introduce a generalization of their result by additionally addressing uncertainty related to the likelihood. We give an upper bound for the posterior probability when both the prior and the likelihood belong to a set of probabilities. Furthermore, we give a sufficient condition for this upper bound to become an equality. This result is interesting on its own, and has the potential of being applied to various fields of engineering (e.g. model predictive control), machine learning, and artificial intelligence.

• Dokumententyp: Konferenzbeitrag (Paper)
• Publikationsform: Publisher's Version
• Fakultät: Mathematik, Informatik und Statistik > Informatik > Künstliche Intelligenz und Maschinelles Lernen
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0302-9743
• Sprache: Englisch