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Uncertainty measures: The big picture

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arxiv 2104.06839 v1 pith:HQ2QXK4D submitted 2021-04-14 math.ST cs.AImath.PRstat.TH

classification math.STcs.AImath.PRstat.TH
keywords uncertaintytheoryprobabilityappraisalargumentsarraybeencharacterised
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Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty have been proposed, many of them generalisations of classical probability. As we show here, such frameworks can be organised into clusters sharing a common rationale, exhibit complex links, and are characterised by different levels of generality. Our goal is a critical appraisal of the current landscape in uncertainty theory.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Epistemic Wrapping for Uncertainty Quantification

    cs.LG 2025-05 reject novelty 6.0 of 10

    A Bayesian weight posterior is wrapped into a belief-function posterior via interval masses and a fitted Dirichlet distribution, then used to initialize a Hybrid Interval Neural Network, with reported accuracy and OOD...

  2. Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'

    cs.AI 2025-05 conditional novelty 3.0 of 10

    Machine learning should use second-order uncertainty measures, such as credal sets and random sets, so models can explicitly represent ignorance and avoid overconfident predictions on unfamiliar data.

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