antimonyanthony’s comment is pretty much what I had in mind. I would also point to Wikipedia on Bayesian epistemology: “It is based on the idea that beliefs can be interpreted as subjective probabilities. As such, they are subject to the laws of probability theory, which act as the norms of rationality.” The key idea is that all beliefs (as opposed to values) should be expressible via probabilities, regardless of what kind of data we have for interrogating them, whether they concern deterministic events, etc.
I definitely don’t mean to imply that Bayesian mindset is incompatible with using frequentist statistical tools. I was more just highlighting the “beliefs = probabilities” idea that I think is at the heart of it.
Thanks for that link. I did not know that this is a term used to describe this viewpoint. I would expect frequentist statisticians to also agree with “beliefs = probabilities”, and when they do so it would feel odd to be able to say they are being (or acting) Bayesian when doing so. They could agree with much of the viewpoint in that Wikipedia page.
Maybe the way I can reconcile this is to think of “Bayesian epistemology” and “Bayesian statistics” as two concepts inspired by the same source but with different breadths. Rather than only using Bayesian as a word to highlight the specific parts of a belief system that can’t be described by general probability, in epistemology we can use Bayesian as a broader term.
antimonyanthony’s comment is pretty much what I had in mind. I would also point to Wikipedia on Bayesian epistemology: “It is based on the idea that beliefs can be interpreted as subjective probabilities. As such, they are subject to the laws of probability theory, which act as the norms of rationality.” The key idea is that all beliefs (as opposed to values) should be expressible via probabilities, regardless of what kind of data we have for interrogating them, whether they concern deterministic events, etc.
I definitely don’t mean to imply that Bayesian mindset is incompatible with using frequentist statistical tools. I was more just highlighting the “beliefs = probabilities” idea that I think is at the heart of it.
Thanks for that link. I did not know that this is a term used to describe this viewpoint. I would expect frequentist statisticians to also agree with “beliefs = probabilities”, and when they do so it would feel odd to be able to say they are being (or acting) Bayesian when doing so. They could agree with much of the viewpoint in that Wikipedia page.
Maybe the way I can reconcile this is to think of “Bayesian epistemology” and “Bayesian statistics” as two concepts inspired by the same source but with different breadths. Rather than only using Bayesian as a word to highlight the specific parts of a belief system that can’t be described by general probability, in epistemology we can use Bayesian as a broader term.