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7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011 Forecasting with Imprecise Probabilities
 

Summary: 7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011
Forecasting with Imprecise Probabilities
Teddy Seidenfeld Mark J. Schervish Joseph B. Kadane
teddy@stat.cmu.edu mark@stat.cmu.edu kadane@stat.cmu.edu
Carnegie Mellon University
Abstract
We review de Finetti's two coherence criteria for
determinate probabilities: coherence1 defined in terms of
previsions for a set of random variables that are
undominated by the status quo previsions immune to a
sure-loss and coherence2 defined in terms of forecasts
for events undominated in Brier score by a rival forecast.
We propose a criterion of IP-coherence2 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 -Maximin
or (Levi's) E-admissibility-+--Maximin we give a

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics