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Coherent conditional probabilities and proper scoring rules

  • Autori: Gilio, A; Sanfilippo, G
  • Anno di pubblicazione: 2011
  • Tipologia: Contributo in atti di convegno pubblicato in volume
  • Parole Chiave: Conditional probability assessments, coherence, penalty criterion, proper scoring rules, conditional scoring rules, weak dominance, strong dominance, admissibility, Bregman divergence, g-coherence, total coherence, imprecise probability assessments.
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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.