Notes on conditional previsions
International Journal of Approximate Reasoning
Probabilistic coherence and proper scoring rules
IEEE Transactions on Information Theory
Proper Scoring Rules, Dominated Forecasts, and Coherence
Decision Analysis
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We review de Finetti's two coherence criteria for determinate probabilities: coherence"1 defined in terms of previsions for a set of events that are undominated by the status quo - previsions immune to a sure-loss - and coherence"2 defined in terms of forecasts for events undominated in Brier score by a rival forecast. We propose a criterion of IP-coherence"2 based on a generalization of Brier score for IP-forecasts that uses 1-sided, lower and upper, probability forecasts. However, whereas Brier score is a strictly proper scoring rule for eliciting determinate probabilities, we show that there is no real-valued strictly proper IP-score. Nonetheless, with respect to either of two decision rules - @C-maximin or (Levi's) E-admissibility-+-@C-maximin - we give a lexicographic strictly proper IP-scoring rule that is based on Brier score.