Forget cleverness for its own sake, optimize for the consequences.
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Capturing that first thought and directing it somewhere useful is crucial
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But two Bayesian inferences from the same data can also give different results. How could this be a non-issue for Bayesian inference while being indicative of a central problem for NHST? (If the answer is that Bayesian inference is rigorously deduced from probability theory's axioms but NHST is not, then the fact that NHST can give different results for the same data is not a true objection, and you might want to rephrase.)
If the OP is read to hold constant everything not mentioned as a difference, that includes the prior beliefs of the person doing the analysis, as against the hypothetical analysis that wasn't performed by that person.
Does "two Bayesian inferences" imply it is two different people making those inferences, with two people not possibly having identical prior beliefs? Could a person performing axiom-obeying Bayesian inference reach different conclusions than that same person hypothetically would have had they performed a different axiom-obeying Bayesian inference?