Timeline for Does a 100% degree of belief imply that no amount of evidence can change your mind?
Current License: CC BY-SA 4.0
13 events
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| Jun 14, 2023 at 15:54 | comment | added | justhalf | Usually I informally call the non-informative prior 0.5 as "Bayesian zero", since if you do this Bayesian update in the logodds domain, it's simply representing an addition operator, and this Bayesian zero acts as the additive identity. In this logodds domain, 100% positive certainty (probability 1) is positive infinity, and 100% negative certainty (probability 0) is negative infinity. So you can see that no matter how many evidences you collect, you won't ever be 100% certain. | |
| Jun 14, 2023 at 15:52 | comment | added | justhalf | @thinkingman as Nobody said, the "neutral" prior for Bayesian philosophy is the non-informative prior, which is 0.5, not zero. A prior of 0.5 says that we do not know anything about this, and have no evidence for or against it. You can say probably when you're born you have this 0.5 prior as your prior for anything. As you grow up, you collect evidences, and your belief is updated. If you talk specifically about a point in your life, where you have collected evidences before, you can also use the "output" of your life experiences up to that point as the prior for the formula now. | |
| Jun 14, 2023 at 15:35 | comment | added | RonJohn | "If I take the view that the prior probability of finding a pink unicorn is zero , and then a herd of them is found grazing in the depths of Nottingham Forest"... sounds like the black swans they found in Australia. | |
| Jun 14, 2023 at 13:44 | comment | added | Nobody | @thinkingman It is not true that "Assigning a non-zero prior would require evidence." If you have no evidence at all, either for or against a proposition, you should assign a non-informative prior, representing complete ignorance. If, on the other hand, by "no evidence" you mean no evidence in favor of a proposition, but possibly some against it, then your prior should be concentrated near zero, but not entirely at zero. How concentrated it should be depends on how much evidence against the proposition you have. | |
| Jun 14, 2023 at 10:52 | comment | added | Scott Rowe | If I can't get my checkbook to balance, but I didn't realize that the bank put in 7 cents of interest, it doesn't mean that there is something wrong with Arithmetic. The plus sign doesn't shout, "It's the Interest, stupid!" What I could do is always include a place for interst, but set it to zero unless I knew otherwise. Same for Fees, deposits from the government, scam checks someone wrote against my account, things clearing from prior statements... Let's just put all of existence in the formula, then it would be correct. And, I would still get some of the inputs wrong... Damnation! | |
| Jun 14, 2023 at 8:44 | comment | added | Professor Sushing | Agreed. There is only any point in applying Bayes' theorem if you can supply it with sensible estimates of the probabilities- ie estimates based on some meaningful rationale that holds water. If all the probabilities involved are just blind guesses, you might as well just guess the overall probability rather than feeding blind guesses into a calculation. | |
| Jun 14, 2023 at 5:52 | comment | added | user62907 | Yeah and that's the part I'm having trouble grappling with. Since to me, if there is no evidence for a theory so far, it seems meaningless to assign it a zero (or a non zero) prior, even if there does end up being evidence for the theory later on | |
| Jun 14, 2023 at 5:37 | comment | added | Professor Sushing | I agree with your general point that the theory is useless for many types of question where you can't meaningfully assign a prior. If we did find pink unicorns then what Bayes' theorem will tell us was that we were definitely wrong in assigning a prior of zero. | |
| Jun 14, 2023 at 5:34 | comment | added | user62907 | In your pink unicorn case, what would have been the "correct" prior then? If you cannot come up with one, doesn't this indicate that this theorem isn't the best for updating your beliefs? Note I am not saying that the formula itself is troublesome since it just has to do with conditional probability. Rather, my beef is with using it to update beliefs | |
| Jun 14, 2023 at 5:33 | comment | added | Professor Sushing | My assessment of the prior would have been wrong in the same way as I would be wrong if I assumed the odds of throwing a six with a fair dice was one in a hundred. | |
| Jun 14, 2023 at 5:32 | comment | added | Professor Sushing | No, it indicates a problem with how we judge the probabilities we need to feed into the theorem. | |
| Jun 14, 2023 at 5:30 | comment | added | user62907 | But in what sense would your assessment of the prior before be wrong? You had never seen pink unicorns and had no evidence for them. Assigning a non zero prior would require evidence. If you can simply assert a non zero prior for unicorns without coming across them, even if there do end up being pink unicorns, it would still be arguably unjustified to assign a non zero prior. But now we're a standstill where it seems to be unjustified to assign both a zero or a non zero prior in the case of undiscovered pink unicorns. Doesn't this indicate a problem with the theorem? | |
| Jun 14, 2023 at 5:27 | history | answered | Professor Sushing | CC BY-SA 4.0 |