Agreed, great post. But I think you are trying to push Bayesian Statistics past what it SHOULD be used for.
Bayesian Statistics are only useful because we approach the correct answer as we gain all the information possible. Only in this limit (of infinite information) is Bayesian useful. Priors based off no information are, well, useless.
Scenario 1: You flip a fair coin and have a 50⁄50 chance of it landing heads
Scenario 2: (to steal xepo’s example) are bloxors greeblic? You have NO IDEA, so your priors are 50⁄50
Even though in both scenarios the chances are 50⁄50, I would feel much more confident betting money on scenario 1 than scenario 2. Therefore my model of choices contains something MORE than probabilities. As far as I know Bayesian statistics just doesn’t convey this NEEDED information. You cant use Bayesian probabilities here in a useful way. It’s the wrong tool for the job.
Even frequentest statistics is useless here.
A lot of day-to-day decisions are based off very limited information. I am not able to lay out a TRUE model of how we intuitively make those decisions but “how much information I have to work with” is definitely an aspect in my mental model that is not entirely captured by Bayes Theorem.
Agreed, great post. But I think you are trying to push Bayesian Statistics past what it SHOULD be used for.
Bayesian Statistics are only useful because we approach the correct answer as we gain all the information possible. Only in this limit (of infinite information) is Bayesian useful. Priors based off no information are, well, useless.
Scenario 1: You flip a fair coin and have a 50⁄50 chance of it landing heads
Scenario 2: (to steal xepo’s example) are bloxors greeblic? You have NO IDEA, so your priors are 50⁄50
Even though in both scenarios the chances are 50⁄50, I would feel much more confident betting money on scenario 1 than scenario 2. Therefore my model of choices contains something MORE than probabilities. As far as I know Bayesian statistics just doesn’t convey this NEEDED information. You cant use Bayesian probabilities here in a useful way. It’s the wrong tool for the job.
Even frequentest statistics is useless here.
A lot of day-to-day decisions are based off very limited information. I am not able to lay out a TRUE model of how we intuitively make those decisions but “how much information I have to work with” is definitely an aspect in my mental model that is not entirely captured by Bayes Theorem.