References
We provide a non-exhaustive list of materials relevant to the course here. If you would like to suggest additional resources for inclusion (including your own work), please feel free to submit a pull request on GitHub or contact us directly by email.
Books
- Statistical Reasoning with Imprecise Probabilities (1990) by Peter Walley
- Introduction to Imprecise Probabilities (2014) by Thomas Augustin, Frank P.A. Coolen, Gert de Cooman, and Matthias C. M. Troffaes
- Lower Previsions (2014) by Matthias C. M. Troffaes and Gert de Cooman
- Inferential Models: Reasoning with Uncertainty (2016) by Ryan Martin and Chuanhai Liu
- The Geometry of Uncertainty: The Geometry of Imprecise Probabilities (2021) by Fabio Cuzzolin
- Introduction to Uncertainty Quantification (2015) by T. J. Sullivan
- Probability and Finance: It’s Only a Game! (2005) by Glenn Shafer and Vladimir Vovk
Articles
- Imprecise Probability, The Stanford Encyclopedia of Philosophy, 2019
- Interpretations of Probability, The Stanford Encyclopedia of Philosophy, 2023
- Introduction to the Theory of Sets of Probabilities by Fabio Cozman
- Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly ‘Know When They Do Not Know’
- A Gentle Approach to Imprecise Probability by Gregory Wheeler
Master and PhD Theses
- Imprecise Probabilities in Machine Learning: Structure and Semantics, Christian Fröhlich, 2025
- Epistemic Deep Learning: Enabling Machine Learning Models to Know When They Do Not Know, Shireen Kudukkil Manchingal, 2025
Review Papers
- Possibilistic Inferential Models: A Review by Ryan Martin (2025)
- Possibility Theory and its Applications: Where Do we Stand ? by Didier Dubois and Henri Prade (2014)
- Decision-Making with Belief Functions: a Review by T. Denœux (2019)
Research Papers
Foundations and Representations of Imprecise Probability
- An introduction to the imprecise Dirichlet model for multinomial data, International Journal of Approximate Reasoning, 2005
- Towards a strictly frequentist theory of imprecise probability, ISIPTA 2023
- Credal Learning Theory, NeurIPS 2024
- Game-Theoretic Statistics and Safe Anytime-Valid Inference, Statistical Science, 2023
- On Individual Risk, Synthese, 2017 (Discuss different interpretations of probability)
- Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss and Simpson’s Paradox, Statistical Science, 2021
Imprecise Classification and Regression
- Learning Sets of Probabilities Through Ensemble Methods, ECSQARU 2023
- Possibilistic Classification by Support Vector Networks, Neural Networks, 2022
- Neural Network Model for Imprecise Regression with Interval Dependent Variables, Neural Networks, 2023
- Possibilistic Instance-based Learning, Artificial Intelligence, 2003
- Reliable Classification: Learning Classifiers that Distinguish Aleatoric and Epistemic Uncertainty, Information Sciences, 2014
- Reliable Multi-class Classification based on Pairwise Epistemic and Aleatoric Uncertainty, IJCAI, 2018
- Weakly-Supervised Contrastive Learning for Imprecise Class Labels, ICML, 2025
- Imprecise Label Learning: A Unified Framework for Learning with Various Imprecise Label Configurations, NeurIPS 2024
- Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification, ICLR, 2025
- Credal Prediction based on Relative Likelihood, NeurIPS 2025
Conformal Prediction
- A Tutorial on Conformal Prediction, JMLR, 2008
- A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification, ArXiv, 2022
- Conformalized Credal Set Predictors, NeurIPS, 2024
- A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification, ArXiv, 2022
- Conformal Prediction Regions are Imprecise Highest Density Regions, ArXiv, 2025
- Conformal Prediction with Partially Labeled Data, ArXiv, 2023
- Learning Calibrated Belief Functions from Conformal Predictions, ISIPTA, 2023
- Validity, Consonant Plausibility Measures, and Conformal Prediction, International Journal of Approximate Reasoning, 2022
- The Joys of Categorical Conformal Prediction, ArXiv 2025
Out-of-Distribution Generalisation
- Domain Generalisation via Imprecise Learning, ICML 2024
Statistical Inference
- Credal Two-sample Tests of Epistemic Uncertainty, AISTATS 2025
- Integral Imprecise Probability Metrics, NeurIPS 2025
- False Confidence, Non-additive Beliefs, and Valid Statistical Inference, IJAR 2019
Possibility Theory
Causality and Causal Inference
- Credal networks, Artificial Intelligence, 2000
- Thirty years of credal networks: Specification, algorithms and complexity, International Journal of Approximate Reasoning, 2020
Uncertainty Quantification
- Quantifying Epistemic Predictive Uncertainty in Conformal Prediction, ArXiv, 2026
- Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?, UAI, 2023
- Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods, Machine Learning, 2021
- Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty? UAI, 2023
- Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation, NeurIPS, 2022
- Quantification of Credal Uncertainty in Machine Learning: A Critical Analysis and Empirical Comparison, UAI, 2022
- Uncertainty Measures: A Critical Survey, Information Fusion, 2024
- Second-order Uncertainty Quantification: A Distance-based Approach, ICML, 2022
Imprecise Probabilistic Forecast and Calibration
- IP Scoring Rules: Foundations and Applications, ISIPTA, 2019
- Evaluating Imprecise Forecasts, ISIPTA, 2023
- IP Scoring Rules: Foundations and Applications, ISIPTA, 2019
- On Second-Order Scoring Rules for Epistemic Uncertainty Quantification, ICML, 2023
- Truthful Elicitation of Imprecise Forecasts, UAI, 2025
- On the Calibration of Probabilistic Classifier Sets, AISTATS, 2023
- Scoring Rules and Calibration for Imprecise Probabilities, ArXiv, 2024
Decision-Making with Imprecise Probability
- Decision Making under Uncertainty using Imprecise Probabilities, International Journal of Approximate Reasoning, 2007
- Archimedean Choice Functions: An Axiomatic Foundation for Imprecise Decision Making, Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2020
- Risk Measures and Upper Probabilities: Coherence and Stratification, JMLR 2024
- Concepts for Decision Making under Severe Uncertainty with Partial Ordinal and Partial Cardinal Preferences, ISIPTA 2017
Multi-Armed Bandit and Reinforcement Learning
Imprecise Probability in Modern ML (Deep Learning, Foundation Models, LLM, GenAI)
- Credal Bayesian Deep Learning, TMLR, 2024
- Aleatoric and Epistemic Uncertainty with Random Forests, Advances in Intelligent Data Analysis, 2020
- Credal Self-Supervised Learning, NeurIPS, 2021
- Imprecise Bayesian optimization, Knowledge-Based Systems, 2024
- Random-Set Large Language Models, ArXiv 2025
- Abductive Reasoning in Logical Credal Networks, NeurIPS, 2024
- Credal Deep Ensembles for Uncertainty Quantification, NeurIPS, 2024
- Evidential Deep Learning to Quantify Classification Uncertainty, NeurIPS, 2018
Use Cases of Imprecise Probability in Fairness, Privacy, Ethics, Safety, etc
- Differential privacy: general inferential limits via intervals of measures, ISIPTA, 2023
- Statistical Comparisons of Classifiers by Generalized Stochastic Dominance, JMLR, 2023
- Distributionally Robust Statistical Verification with Imprecise Neural Networks, HSCC, 2024
- Imprecise Probability for Non-commuting Observables, New Journal of Physics, 2015
Related Courses
The teaching materials for this course were partly inspired by those used in the following courses:
- ST790: Imprecise-Probabilistic Foundations of Statistics & Data Science by Ryan Martin
- Uncertainty Representation and Reasoning (2AMU30) by Erik Quaeghebeur and Vu-Linh Nguyen
- Theory of Belief Functions: Application to Machine Learning and Statistical Inference by Thierry Denoeux