While I understand that frequentism is based on the ratio of events, but I didn’t think it precluded making probabilistic opinions before any data exists. Can you explain more about how that is a ramification of frequentism? I suppose a frequentist might not ever say something is 20% likely in the absence of data or a proof that the outcome is 20% likely by definition. They might instead construct a hypothesis, which could be that something is 20% likely, and say that they can’t confidently reject the hypothesis. Although I’m not sure a typical Bayesian would literally say something is 20% likely either, but rather that they think something is 20% likely.
The example that followed in the text, to derive one person’s estimate of the likelihood of some future event happening by imagining bets, seems like a tool that would work no matter how that person came to their probability estimates. And in the example the author reached that opinion through “pretty much pure intuition”, which seems neither specifically frequentist or Bayesian. Although it does seem more Bayesian to acknowledge intuition as an acceptable prior.
I read #1 as arguing for assigning specific meaning to claims, setting up the problem in a way that can be quantified, ‘the “meaning” of a statement mostly comes down to what specific, visualizable, falsifiable predictions it points to’. That applies to frequentist people too.
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.
While I understand that frequentism is based on the ratio of events, but I didn’t think it precluded making probabilistic opinions before any data exists. Can you explain more about how that is a ramification of frequentism? I suppose a frequentist might not ever say something is 20% likely in the absence of data or a proof that the outcome is 20% likely by definition. They might instead construct a hypothesis, which could be that something is 20% likely, and say that they can’t confidently reject the hypothesis. Although I’m not sure a typical Bayesian would literally say something is 20% likely either, but rather that they think something is 20% likely.
The example that followed in the text, to derive one person’s estimate of the likelihood of some future event happening by imagining bets, seems like a tool that would work no matter how that person came to their probability estimates. And in the example the author reached that opinion through “pretty much pure intuition”, which seems neither specifically frequentist or Bayesian. Although it does seem more Bayesian to acknowledge intuition as an acceptable prior.
I read #1 as arguing for assigning specific meaning to claims, setting up the problem in a way that can be quantified, ‘the “meaning” of a statement mostly comes down to what specific, visualizable, falsifiable predictions it points to’. That applies to frequentist people too.
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.