Expert Opinions in Safety Studies. Volume 4. A Theory of Weight for Combining Expert Opinion

摘要

The notion of scoring rules for average probabilities is introduced. A representation theorem for differentiable scoring rules is proved. On the basis of this notion a theory of weights is given which reward good calibration and low entropy, either in the sample distribution or in the assessed distribution. The weights incorporate the idea that expert probability assessors should be regarded as statistical hypotheses and weighted via traditional significance testing. Strong and weak asymptotic propriety of scoring rules is defined, and asymptotic results are obtained.