The proper scientific interpretation of the seismic hazard estimates requires a probabilistic framework that admits epistemic uncertainties on aleatory variables. This is not straightforward because, to subjectivists, all probabilities are epistemic, whereas to frequentists, all probabilities are aleatory.We illustrate the inadequacy of purely subjectivist and purely frequentist interpretations of probability by examining the probabilistic meaning of the mean hazard. We advocate a unified approach based on experimental concepts that define aleatory variability in terms of exchangeable sequences of observations, and we show how experimental concepts allow testing of models based on expert opinion by frequentist methods. © 2017, Seismological Society of America. All rights reserved.