In this paper we study the relationship between the notion of coherence for conditional probability assessments on a family of conditional events and the notion of admissibility with respect to scoring rules. By extending a recent result given in literature for unconditional events, we prove, for any given strictly proper scoring rule s, the equivalence between the coherence of a conditional probability assessment and its admissibility with respect to s. In this paper we focus our analysis on the case of continuous bounded scoring rules. In this context a key role is also played by Bregman divergence and by a related theoretical aspect. Finally, we briefly illustrate a possible way of defining (generalized) coherence of interval-valued probability assessments by exploiting the notion of admissibility given for precise probability assessments.

Gilio, A., Sanfilippo, G. (2011). Coherent conditional probabilities and proper scoring rules. In F. Coolen, G. De Cooman, T. Fetz, M. Oberguggenberger (a cura di), ISIPTA '11. Proceedings of the Seventh International Symposium on Imprecise Probability: Theories and Applications. (pp. 189-198). Innsbruck : STUDIA.

Coherent conditional probabilities and proper scoring rules

SANFILIPPO, Giuseppe
2011-01-01

Abstract

In this paper we study the relationship between the notion of coherence for conditional probability assessments on a family of conditional events and the notion of admissibility with respect to scoring rules. By extending a recent result given in literature for unconditional events, we prove, for any given strictly proper scoring rule s, the equivalence between the coherence of a conditional probability assessment and its admissibility with respect to s. In this paper we focus our analysis on the case of continuous bounded scoring rules. In this context a key role is also played by Bregman divergence and by a related theoretical aspect. Finally, we briefly illustrate a possible way of defining (generalized) coherence of interval-valued probability assessments by exploiting the notion of admissibility given for precise probability assessments.
2011
Settore MAT/06 - Probabilita' E Statistica Matematica
978-3-902652-40-9
Gilio, A., Sanfilippo, G. (2011). Coherent conditional probabilities and proper scoring rules. In F. Coolen, G. De Cooman, T. Fetz, M. Oberguggenberger (a cura di), ISIPTA '11. Proceedings of the Seventh International Symposium on Imprecise Probability: Theories and Applications. (pp. 189-198). Innsbruck : STUDIA.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/62335
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