This is simply wrong. Bayesian statistics is just Bayesian probability theory. As is Bayesian epistemology. Bayesian probabilities are epistemic probabilities.
I don’t think there is a “Bayesian” probability theory. There is Kolmogorov’s axiomatization of probability theory, and there is the subjective interpretation of probability, but those are not necessary or sufficient for Bayesian epistemology or Bayesian statistics. Bayesian statistics contains a lot of specific methodology and concepts, like credible intervals, and Bayesian epistemology contains normative principles like conditionalization which do not follow from the axioms. Experts on either likely haven’t heard of the other. Books on Bayesian statistics and Bayesian epistemology contain very very different material.
The fact that people tend to specialize in one or the other does not mean that “the two have little to do with each other.” Likewise, there are physicists who spend a lot of time working in foundations and interpretation of QM, and others who spend their time applying it to solve problems in solid state physics, nuclear physics, etc. They’re working on different kinds of problems, but it’s absurd to say that the two have “little to do with each other.”
But do look at introductions to Bayesian statistics versus Bayesian epistemology. There does exist hardly any overlap. One thing they have in common is that they both agree that it makes sense to assign probabilities to hypotheses. But otherwise? I personally know quite a lot about Bayesian epistemology, but basically none of that appears to be of interest for Bayesian statisticians.
This is simply wrong. Bayesian statistics is just Bayesian probability theory. As is Bayesian epistemology. Bayesian probabilities are epistemic probabilities.
I don’t think there is a “Bayesian” probability theory. There is Kolmogorov’s axiomatization of probability theory, and there is the subjective interpretation of probability, but those are not necessary or sufficient for Bayesian epistemology or Bayesian statistics. Bayesian statistics contains a lot of specific methodology and concepts, like credible intervals, and Bayesian epistemology contains normative principles like conditionalization which do not follow from the axioms. Experts on either likely haven’t heard of the other. Books on Bayesian statistics and Bayesian epistemology contain very very different material.
Edit: Just look at introductions to Bayesian statistics and Bayesian epistemology.
The fact that people tend to specialize in one or the other does not mean that “the two have little to do with each other.” Likewise, there are physicists who spend a lot of time working in foundations and interpretation of QM, and others who spend their time applying it to solve problems in solid state physics, nuclear physics, etc. They’re working on different kinds of problems, but it’s absurd to say that the two have “little to do with each other.”
But do look at introductions to Bayesian statistics versus Bayesian epistemology. There does exist hardly any overlap. One thing they have in common is that they both agree that it makes sense to assign probabilities to hypotheses. But otherwise? I personally know quite a lot about Bayesian epistemology, but basically none of that appears to be of interest for Bayesian statisticians.