This paper investigates de Finetti’s coherence as an opera- tional foundation for a wide range of non-additive uncertainty measures and focuses, in particular, on Belief functions and Lower probabilities. In a companion paper we identify a number of non-limiting circumstances under which Dutch Book criteria for Belief functions and Lower proba- bility are undistinguishable, which is surprising given that Lower prob- abilities are known to exist which do no satisfy the axioms of Belief functions. The main contribution of this paper consists in putting for- ward a comparison between a criterion based on the Brier scoring rule for Belief Functions and the scoring rule introduced in 2012 by Seidenfeld, Schervish and Kadane for Imprecise probabilities. Through this compar- ison we show that scoring rules allow us to distinguish coherence-wise between Belief functions and Imprecise probabilities.

Scoring Rules for Belief Functions and Imprecise Probabilities: A Comparison / E.A. Corsi, T. Flaminio, H. Hosni (LECTURE NOTES IN ARTIFICIAL INTELLIGENCE). - In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty / [a cura di] J. Vejnarová, N. Wilson. - [s.l] : Springer, 2021. - ISBN 978-3-030-86771-3. - pp. 301-313 (( Intervento presentato al 16. convegno ECSQARU tenutosi a Prague nel 2021 [10.1007/978-3-030-86772-0_22].

Scoring Rules for Belief Functions and Imprecise Probabilities: A Comparison

E.A. Corsi;H. Hosni
2021

Abstract

This paper investigates de Finetti’s coherence as an opera- tional foundation for a wide range of non-additive uncertainty measures and focuses, in particular, on Belief functions and Lower probabilities. In a companion paper we identify a number of non-limiting circumstances under which Dutch Book criteria for Belief functions and Lower proba- bility are undistinguishable, which is surprising given that Lower prob- abilities are known to exist which do no satisfy the axioms of Belief functions. The main contribution of this paper consists in putting for- ward a comparison between a criterion based on the Brier scoring rule for Belief Functions and the scoring rule introduced in 2012 by Seidenfeld, Schervish and Kadane for Imprecise probabilities. Through this compar- ison we show that scoring rules allow us to distinguish coherence-wise between Belief functions and Imprecise probabilities.
Scoring rules; Belief functions; Lower probabilities; Imprecise probabilities; Coherence
Settore M-FIL/02 - Logica e Filosofia della Scienza
Settore MAT/01 - Logica Matematica
DECC18LBIAN_01 - Dipartimenti di Eccellenza 2018-2022 - Dipartimento di FILOSOFIA - BIANCHI, LUCA MARIA - DECC - Bando Dipartimenti di Eccellenza - 2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/871297
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