(It’s subject to limitations that do not constrain the Bayesian approach, and as near as I can tell, is mathematically equivalent to a non-informative Bayesian approach when it is applicable, but the author’s justification for his procedure is wholly non-Bayesian.)
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?)
Here’s one way.
(It’s subject to limitations that do not constrain the Bayesian approach, and as near as I can tell, is mathematically equivalent to a non-informative Bayesian approach when it is applicable, but the author’s justification for his procedure is wholly non-Bayesian.)
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: