Property Elicitation on Imprecise Probabilities

James Bailie; Rabanus Derr

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arXiv · 2507.05857

Property Elicitation on Imprecise Probabilities

James Bailie·Rabanus Derr

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Abstract

Property elicitation studies which attributes of a probability distribution can be determined by minimizing a risk. We investigate a generalization of property elicitation to imprecise probabilities (IP). This investigation is motivated by distributionally robust optimization and multi-distribution learning. Both those frameworks replace the minimization of a single risk over a (precise) probability by a maximin risk minimization over a set of probabilities -- i.e. an IP. We show what can be learned in those multi-distribution setups by providing necessary and sufficient conditions for the elicitability of an IP-property. Central to these conditions is the observation made in related literature that the elicited IP-property is the corresponding classical property of the probability in the IP with the maximum Bayes risk.

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James Bailie, Rabanus Derr. 2025-07-08. Property Elicitation on Imprecise Probabilities. https://arxiv.org/abs/2507.05857

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