Excursion 1 Tour II: Error Probing Tools vs. Logics of Evidence
Blurb. Core battles revolve around the relevance of a method’s error probabilities. What’s distinctive about the severe testing account is that it uses error probabilities evidentially: to assess how severely a claim has passed a test. Error control is necessary but not sufficient for severity. Logics of induction focus on the relationships between given data and hypotheses–so outcomes other than the one observed drop out. This is captured in the Likelihood Principle (LP). Tour II takes us to the crux of central wars in relation to the Law of Likelihood (LL) and Bayesian probabilism. (1.4) Hypotheses deliberately designed to accord with the data can result in minimal severity. The likelihoodist wishes to oust them via degrees of belief captured in prior probabilities. To the severe tester, such gambits directly alter the evidence by leading to inseverity. (1.5) Stopping rules: If a tester tries and tries again until significance is reached–optional stopping–significance will be attained erroneously with high probability. According to the LP, the stopping rule doesn’t alter evidence. The irrelevance of optional stopping is an asset for holders of the LP, it’s the opposite for a severe tester. The warring sides talk past each other. Continue reading