[gaur]

I guess a hard-line frequentist (if such a person exists) would counter that you can't assign probabilities to hypotheses or fixed parameters. Then Bayes's theorem (and every other statement about probability) is true only when applied to statements about how often a certain event will occur.

But of course, most people do assign probabilities to hypotheses and fixed parameters, even if only informally. Bayesian probability theory is an attempt to formalize that kind of intuitive reasoning.

[nshepperd]

I have heard of people genuinely saying such a thing. Fortunately, it is nothing but an empty redefinition of the word "probability". In fact, rational degrees of belief in hypotheses do follow the kolmogorov axioms (as shown by eg. Cox's theorem or the VNM theorem), and bayes theorem does therefore apply. Whether or not someone refuses to call that "probability" makes no difference.

[lottin]

I think it's strange this sudden comeback of a theory that was dismissed more than 70 years ago by Fisher and many others, but no one, as far as I know, cares to explain why Fisher was wrong and why the theory is right. It makes me very suspicious, to be honest.

[dragandj]

Actually, many Bayesian textbooks cover that. Try Jaynes - Probability Theory: The Logic of Science.

[eli_gottlieb]

>I guess a hard-line frequentist (if such a person exists) would counter that you can't assign probabilities to hypotheses or fixed parameters. Then Bayes's theorem (and every other statement about probability) is true only when applied to statements about how often a certain event will occur.

If you model "thinking" and "believing" as sampling in probabilistic programs (which they do in some schools of cognitive science), then Bayes' Theorem becomes a theorem about how often certain execution traces occur when the sampling program is run with fresh randomness. You then need none of the weird metaphysics associated with "subjective Bayesianism".