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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.

Good write-up. Something that has been nagging at me since reading is that I'm not sure this is specifically Bayesian. It's not incompatible with Bayesian viewpoints, yet not exclusive to them either. When I try to describe this type of thinking to people I use the term "probabilistic". In the Venn diagram of viewpoints, the "Bayesian" circle would fit entirely within the "probabilistic" circle. A non-Bayesian, such as someone with a frequentist interpretation of statistics, would still fit all of the reasoning given. This mindset would feel more Bayesian if anything depended on informed priors, or used a Bayesian updating formula, or directly cited Bayes theorem. Maybe what we need is a word for someone who believes in probabilistic rather than certain outcomes.

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.