Historically, the probability calculus began with repeated trials: throws of a fair die, etc. Independent and identically distributed (iid) random variables still populate elementary textbooks, but most statistical models permit variation and dependence in probabilities. Already in 1816, Pierre Simon Laplace explained that nature does not follow any constant probability law; its error laws vary with the nature of measurement instruments and with all the circumstances that accompany them. In 1960, Jerzy Neyman explained that scientific applications had moved into a phase of dynamic indeterminism, in which stochastic processes replace iid models.

Statisticians who call themselves “frequentists” have proposed two competing principles to support the inferences about parameters in stochastic processes and other complex probability models. First, the repeated sampling principle: assess statistical procedures by their behavior in hypothetical repetitions under the same conditions. Second, Cournot’s principle: justify inferences by statements to which the model gives high probability. Cox and Hinkley coined the name “repeated sampling principle” in 1974. The name “Cournot’s principle” was first current in the 1950s. But both ideas are much older. When interpreted as pragmatic instructions, the two principles are more or less equivalent. But they can also be interpreted as philosophical justifications – even as explanations of the meaning of probability models – and then they seem very different. Questions for the panel include the following.