mlsanityData to 14 Oct 2026

A Novel Bayes' Theorem for Upper Probabilities

arXiv 2307.06831 ↗First posted 13 Jul 2023stat.ML cs.LGcited by 13

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Abstract (arXiv)

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 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.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 9 of its 33 references that are in the map. First posted on arXiv 13 Jul 2023.

Builds on

9 of 33 references.

References · 9

  1. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
  2. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 913
  3. 2018Understanding Measures of Uncertainty for Adversarial Example Detectioncited by 177
  4. 2022Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?cited by 125
  5. 2014Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing Itcited by 95
  6. 2022On Uncertainty, Tempering, and Data Augmentation in Bayesian Classificationcited by 46
  7. 2023Credal Bayesian Deep Learningcited by 45
  8. 2023Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?cited by 40
  9. 2017Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradoxcited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 5; 2025: 4; 2026: 2.

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  1. 2023Second-Order Uncertainty Quantification: A Distance-Based Approachcited by 35
  2. 2024Credal Learning Theorycited by 31
  3. 2024From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimationcited by 28
  4. 2024Conformalized Credal Regions for Classification with Ambiguous Ground Truthcited by 19
  5. 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
  6. 2024Statistical Multicriteria Benchmarking via the GSD-Frontcited by 11
  7. 2025Integral Imprecise Probability Metricscited by 11
  8. 2024Uncertainty-based Offline Variational Bayesian Reinforcement Learning for Robustness under Diverse Data Corruptionscited by 8
  9. 2025Credal and Interval Deep Evidential Classificationscited by 8
  10. 2025Conformal Prediction Regions are Imprecise Highest Density Regionscited by 7
  11. 2026Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometrycited by 4
  12. 2025Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluationcited by 2
1 more
  1. 2026Robust Predictive Uncertainty and Double Descent in Contaminated Bayesian Random Featurescited by 0