My take is that we need to base the reasoning on a theorem based on Bayes extended rule by dealing with a number of hypotheses. Ideally all but one is shown to be improbable by a strong likelihood ratio between the target hypothesis and each of its rivals. A different item of evidence may be needed to do this for each rival.

I also agree with Deborah Mayo that one prior and one likelihood ratio with Bayes simple (non-extended) rule is not enough to do this.

]]>“Data x0 do not provide good evidence for hypothesis H if x0 results from a test procedure with a very low probability or capacity of having uncovered the falsity of H, even if H is incorrect.”

Severe testing was a term first coined by Popper and extended by Mayo to frequentist statistics (error probabilities). ]]>