The non-existence in Bayesianism of alternative-free hypothesis tests is not a shortcoming

Bayesian methods of hypothesis testing are comparative, and require hypotheses to be tested against each other with their probabilities summing to unity. In contrast the non-Bayesian literature contains tests for rejecting a hypothesis in isolation. Based on experimental data, intuition is also capable of rejecting (or accepting) a hypothesis in the absence of an alternative. Do non-Bayesian methods therefore encapsulate a principle of reasoning that is missing from Bayesian techniques? No: in such situations, data that spectacularly misfit a theory inspire a new hypothesis (often a generalisation of the old) that is more consistent with the data, and neither Bayesian nor non-Bayesian methods contain any principle for doing that. Alternative-free tests are inequivalent to Bayes’ theorem, which has unique grounding in rationality. Such tests are therefore liable to mislead; this is demonstrated by example. A freshly inspired hypothesis should always be tested against the original in a Bayesian comparison. ...