A Novel Bayes' Theorem for Upper Probabilities

MCML Authors

Yusuf Sale

→ Group Eyke Hüllermeier
 Artificial Intelligence and Machine Learning

Eyke Hüllermeier

Prof. Dr.

Principal Investigator

Artificial Intelligence and Machine Learning

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.

inproceedings

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Epi UAI 2023

International Workshop on Epistemic Uncertainty in Artificial Intelligence. Pittsburgh, PA, USA, Aug 04, 2023.

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Authors

M. Caprio • Y. Sale • E. Hüllermeier • I. Lee

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Links

DOI

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Research Area

 A3 | Computational Models