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The intersection probability: betting with probability intervals
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Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty, as the most natural such transformation. We recall its rationale and definition, compare it with other candidate representives of systems of probability intervals, discuss its credal rationale as focus of a pair of simplices in the probability simplex, and outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.
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Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'
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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