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Erschienen in:
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2024 | OriginalPaper | Buchkapitel

A Novel Bayes’ Theorem for Upper Probabilities

verfasst von : Michele Caprio, Yusuf Sale, Eyke Hüllermeier, Insup Lee

Erschienen in: Epistemic Uncertainty in Artificial Intelligence

Verlag: Springer Nature Switzerland

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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 \(\mathcal {P}\) 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.

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Nächstes Kapitel Deep Learning and MCMC with aggVAE for Shifting Administrative Boundaries: Mapping Malaria Prevalence in Kenya
Fußnoten
1
Recall that in the weak\(^\star \) topology, a net \((P_\alpha )_{\alpha \in I}\) converges to P if and only if \(P_\alpha (A) \rightarrow P(A)\), for all \(A \in \mathcal {F}\). See also results presented in [29, Appendix D3].
 
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Metadaten
Titel
A Novel Bayes’ Theorem for Upper Probabilities
verfasst von
Michele Caprio
Yusuf Sale
Eyke Hüllermeier
Insup Lee
Copyright-Jahr
2024
Buch
Epistemic Uncertainty in Artificial Intelligence

Print ISBN: 978-3-031-57962-2

Electronic ISBN: 978-3-031-57963-9

Copyright-Jahr: 2024

DOI
https://doi.org/10.1007/978-3-031-57963-9_1

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