A long tradition suggests a fundamental distinction between situations of risk, where true objective probabilities are known, and unmeasurable uncertainties where no such probabilities are given. This distinction can be captured in a Bayesian model where uncertainty is represented by the...

We show that a simple "reputation-style" test can always identify which of two experts is informed about the true distribution. The test presumes no prior knowledge of the true distribution, achieves any desired degree of precision in some fixed finite time, and does not use "counterfactual"...

We study the problem of testing an expert whose theory has a learnable and predictive parametric representation, as do standard processes used in statistics. We design a test in which the expert is required to submit a date T by which he will have learned enough to deliver a sharp, testable...