(A more "Bayesian" alternative to model checking is to have an explicit "none of the above" hypothesis as part of your prior.)
I don't see how that's possible. How do you compute the likelihood of the NOTA hypothesis given the data?
NOTA is not well-specified in the general case, but in at least one specific case it's been done. Jaynes's student Larry Bretthorst made a useable NOTA hypothesis in a simplified version of a radar target identification problem (link to a pdf of the doc).
(Somewhat bizarrely, the same sort of approach could probably be made to work in certain problems in proteomics in which the data-generating process shares the key features of the data-generating process in Bretthorst's simplified problem.)
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