finally reading Mayo's Statistical Inference as Severe Testing

perhaps naive question: why isn't inference using the empirical cdf the default for bayesians (and also severe testers)? #statstwitter

i suppose the severe tester can probably do some sort of out of sample goodness of fit test and throw out the ecdf? what's the bayes justification for not using the ecdf?

(Actually, I'm more curious what a likelihoodist does here. I think the "use a prior" is a cop-out non-answer in practice.)