I guess we can agree that the most rational response would be to enter a state of aporia until sufficient evidence is at hand.
and
It sounds like a fine Bayesian approach for getting through life, but for real scientific knowledge, we can’t rely on prior reasonings (even though these might involve Bayesian reasoning). Real science works by investigating evidence.
look like a significant misunderstanding of what the bayesian approach is.
I do not know the answer to you question. Here is my best guess after a couple minutes of trying to answer the question.
Short answer: Bayesianism is not about priors, it is about how evidence should change priors.
The Bayesian approach is all about evidence. Bayesian probability theory is the math of evidence. It needs a prior to work, because evidence is all about how much beliefs should change, so you need a prior to change. You could also do a lot of the Bayesian analysis without choosing a prior, and just write it down as “how much your beliefs would change.” (but this doesn’t end up with answers that are single numbers)
Seriously, if you define evidence as “something that sways your beliefs because it is more likely to happen under one hypothesis than the alternative hypothesis,” then Bayesianism is the math of evidence, and frequentism (which is used in “Real science”) is not. (and does not even really try to be)
Also, most of the people here would agree that if they do not have sufficient evidence, then they should still assign a probability, and you should be very quick to change it as you get evidence. This last claim might be controversial here, because people might have alternate hacks where they don’t do this to avoid bias, but they will agree that if they could trust themselves, they would want to do this.
Seriously, if you define evidence as “something that sways your beliefs because it is more likely to happen under one hypothesis than the alternative hypothesis,” then Bayesianism is the math of evidence, and frequentism (which is used in “Real science”) is not. (and does not even really try to be)
This looks seriously misleading to me. While it may be technically correct (because neither frequentism nor “Real science” care much about swaying your beliefs), the math of deciding what’s “more likely to happen under one hypothesis than the alternative hypothesis” is a standard part of frequentist statistics where it goes by the name of maximum likelihood.
My guess is that it is because
and
look like a significant misunderstanding of what the bayesian approach is.
So, what doc on the web would most concisely rid me of exactly my misunderstanding?
I do not know the answer to you question. Here is my best guess after a couple minutes of trying to answer the question.
Short answer: Bayesianism is not about priors, it is about how evidence should change priors.
The Bayesian approach is all about evidence. Bayesian probability theory is the math of evidence. It needs a prior to work, because evidence is all about how much beliefs should change, so you need a prior to change. You could also do a lot of the Bayesian analysis without choosing a prior, and just write it down as “how much your beliefs would change.” (but this doesn’t end up with answers that are single numbers)
Seriously, if you define evidence as “something that sways your beliefs because it is more likely to happen under one hypothesis than the alternative hypothesis,” then Bayesianism is the math of evidence, and frequentism (which is used in “Real science”) is not. (and does not even really try to be)
Also, most of the people here would agree that if they do not have sufficient evidence, then they should still assign a probability, and you should be very quick to change it as you get evidence. This last claim might be controversial here, because people might have alternate hacks where they don’t do this to avoid bias, but they will agree that if they could trust themselves, they would want to do this.
This looks seriously misleading to me. While it may be technically correct (because neither frequentism nor “Real science” care much about swaying your beliefs), the math of deciding what’s “more likely to happen under one hypothesis than the alternative hypothesis” is a standard part of frequentist statistics where it goes by the name of maximum likelihood.
You might also be interested in the concept of Fisher information.
I agree with you criticism. Thank you.