At least based on #2, it does seem fair to call it âBayesianâ in contrast to frequentist philosophy, since the following objection sounds like a classic frequentist view:
One relatively common viewpoint would say something like: âNo. In order to say something is 20% likely, you ought to have data showing that it happens about 20% of the time. Or some rigorous, experiment-backed statistical model that predicts 20%. You canât just describe some future event, close your eyes and think about it, call it 20% likely, and have that mean anything.â
I used to TA an introductory stats class, and when I had to teach the frequentist concepts like confidence intervals, the lesson plans would very firmly hammer in the idea that the probability of some fixed parameter of nature having a given value is either 0 or 1, we just donât know which one. Frequentists donât endorse assigning probabilities to deterministic and unprecedented events in the future. (In case this is useful, I wrote/âranted about this and other upshots of Bayesianism here.)
Arguably #1 is also especially Bayesian: the point is that your credence in some belief should be proportional to how much more likely some anticipated observations would be given that belief, than given its negation. Thatâs just the likelihood ratio in Bayesian updating.
While I understand that frequentism is based on the ratio of events, but I didnât 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 canât confidently reject the hypothesis. Although Iâm 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 personâs 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 âpretty much pure intuitionâ, 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, âthe âmeaningâ of a statement mostly comes down to what specific, visualizable, falsifiable predictions it points toâ. That applies to frequentist people too.
antimonyanthonyâs comment is pretty much what I had in mind. I would also point to Wikipedia on Bayesian epistemology: âIt 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.â 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 donât mean to imply that Bayesian mindset is incompatible with using frequentist statistical tools. I was more just highlighting the âbeliefs = probabilitiesâ 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 âbeliefs = probabilitiesâ, 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 âBayesian epistemologyâ and âBayesian statisticsâ 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 canât be described by general probability, in epistemology we can use Bayesian as a broader term.
At least based on #2, it does seem fair to call it âBayesianâ in contrast to frequentist philosophy, since the following objection sounds like a classic frequentist view:
I used to TA an introductory stats class, and when I had to teach the frequentist concepts like confidence intervals, the lesson plans would very firmly hammer in the idea that the probability of some fixed parameter of nature having a given value is either 0 or 1, we just donât know which one. Frequentists donât endorse assigning probabilities to deterministic and unprecedented events in the future. (In case this is useful, I wrote/âranted about this and other upshots of Bayesianism here.)
Arguably #1 is also especially Bayesian: the point is that your credence in some belief should be proportional to how much more likely some anticipated observations would be given that belief, than given its negation. Thatâs just the likelihood ratio in Bayesian updating.
While I understand that frequentism is based on the ratio of events, but I didnât 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 canât confidently reject the hypothesis. Although Iâm 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 personâs 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 âpretty much pure intuitionâ, 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, âthe âmeaningâ of a statement mostly comes down to what specific, visualizable, falsifiable predictions it points toâ. That applies to frequentist people too.
antimonyanthonyâs comment is pretty much what I had in mind. I would also point to Wikipedia on Bayesian epistemology: âIt 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.â 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 donât mean to imply that Bayesian mindset is incompatible with using frequentist statistical tools. I was more just highlighting the âbeliefs = probabilitiesâ 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 âbeliefs = probabilitiesâ, 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 âBayesian epistemologyâ and âBayesian statisticsâ 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 canât be described by general probability, in epistemology we can use Bayesian as a broader term.