 Genin and Kelly provide a characterization theorem that provides necessary and sufficient conditions for a set of statistical hypotheses to be identifiable in chance, analogous to the structural conditions we discussed in  Section 3.3  [2017; Theorem 4.3]. Genin [2018] discusses a statistical analogue of the requirement of minimizing mind changes. Recall that a regressive mind change occurs when an inquirer abandons a true hypothesis in favor of a false one  Section 4.3.  The probabilistic analogue is a chance reversal, which occurs when the chance of conjecturing a true hypotheses decreases as the sample size increases. For instance, consider the question of whether a vaccine is effective for an infectious disease. Suppose the vaccine manufacture runs a trial with 1000 patients and has designed a statistical method that has a chance of 90% of correctly indicating that the vaccine is effective when that is indeed the case. Now another trial is run with 1500 patients using the same statistical method. A chance reversal would occur if the method’s chance of correctly indicating that the vaccine is effective drops to 80%. As this example illustrates, a chance reversal corresponds to a failure to replicate a true result. A chance reversal is illustrated in the Figure above, where the chance of conjecturing the true hypothesis is smaller for 2 samples than for 3. Although chance reversals are clearly undesirable, they are difficult to avoid, and in fact commonly used statistical methods are liable to such reversals [Genin 2018]. A more feasible goal is to bound the reversals by a threshold \(t\), such that if the chance of conjecturing the truth does decreases with increasing sample size, it decreases by at most \(t.\) (In symbols, \(P_{n,p}(H) - P_{n+1,p}(H) \lt t\) for all sample sizes \(n\) and true bias values \(p\), where \(H\) is the hypothesis correct for \(p\).) Genin [2018] shows that bounded chance reversal are feasible in many situations, and provides an Ockham theorem that elucidates the constraints that bounding chance reversals provides on statistical hypothesis learning. 