I think you mixed up Bayes’ Theorem and Bayesian Epistemology. The abstract begins:
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution.
They have a problem with a prior distribution, and wish to do without it. That’s what I think the paper is about. The abstract does not say “we don’t like bayes’ theorem and figured out a way to avoid it.” Did you have something else in mind? What?
I had in mind a way of putting probability distributions on unknown constants that avoids prior distributions and Bayes’ theorem. I though that this would answer the question you posed when you wrote:
It’s not specifically about the Bayesian approach in that it applies to various non-Bayesian probabilistic approaches (whatever those may be. can you think of any other approaches besides Bayesian epistemology that you think this is targeted at?)
I think you mixed up Bayes’ Theorem and Bayesian Epistemology. The abstract begins:
They have a problem with a prior distribution, and wish to do without it. That’s what I think the paper is about. The abstract does not say “we don’t like bayes’ theorem and figured out a way to avoid it.” Did you have something else in mind? What?
I had in mind a way of putting probability distributions on unknown constants that avoids prior distributions and Bayes’ theorem. I though that this would answer the question you posed when you wrote: