The uncertainty in earthquake conditional probabilities

The Working Group on California Earthquake Probabilities (WGCEP) questioned the relevance of uncertainty intervals assigned to earthquake conditional probabilities on the basis that the uncertainty in the probability estimate seemed to be greater the smaller the intrinsic breadth of the recurrence-interval distribution. I show here that this paradox depends upon a faulty measure of uncertainty in the conditional probability and that with a proper measure of uncertainty no paradox exists. I also challenge the assertion that the WGCEP probability assessment in 1988 correctly forecast the 1989 Loma Prieta earthquake by showing that posterior probability of rupture inferred after the occurrence of the earthquake from the prior WGCEP probability distribution reverts to a nearly informationless distribution.