Timeline for Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals
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| Apr 10 at 1:41 | comment | added | civilstat | ...In other words, a responsible scientist will help readers distinguish between "I see the sampling error was low; the prior didn't swamp the data; so these results are robust even if I might have preferred a slightly different prior than yours" -- vs -- "I see the sampling error was huge but the credible interval is narrow anyways, meaning the prior must have played a huge role, so now I need to think really hard about how much I (the reader) agree with your (the author's) prior before I trust the results." | |
| Apr 10 at 1:33 | comment | added | civilstat | ...If you only report a Bayesian credible interval, then you don't separate out "sampling error due to the study design" from "epistemic precision due to the prior." If you say "just trust my credible interval" and you refuse to provide any summary of how much sampling error alone may have affected your study results, that's really no different than refusing to tell us whether you used a bathroom scale or kitchen scale to weigh the mice. | |
| Apr 10 at 1:26 | comment | added | civilstat | I agree with @benrg. A frequentist CI is a statement about the study design, not about the parameter -- and that's a feature, not a bug! If study the weights of lab mice, I should report the measurement-unit precision of the scale used to weigh them (a bathroom scale accurate to within 1 pound? a kitchen scale accurate to within 0.1 grams? etc). Similarly, I should report the statistical precision of the experimental design I used: based on sample size, blocking, etc., what was my freq'ist margin of error for the mean? This is worth reporting even if you also want a credible interval. | |
| Mar 1, 2022 at 6:24 | comment | added | Dikran Marsupial | Bayesian credible intervals do not necessarily contain experimenter's biases (and frequentist analyses are not necessarily free of them). You can't necessarily compute a credible interval from your own priors and a frequentist confidence interval. | |
| Mar 1, 2022 at 1:22 | comment | added | benrg | @DikranMarsupial I said the same thing in the paragraph beginning "That isn't what you really want to know." You want a credible interval that you calculated yourself from your own priors and the confidence interval in the paper. You don't want a credible interval that reflects the experimenters' biases instead of yours. If it's approved by a theorist and you're just a layperson then that's different, but that's more like popular science reporting than the peer-reviewed literature. | |
| Feb 28, 2022 at 22:11 | comment | added | Dikran Marsupial | I don't see how the rest of the answer substantiates the claim "any paper in experimental science". Most often in experimental science, what you really want to know is what you can infer from the outcome of the particular experiment that you actually performed, and that is summarised by the credible interval. Very rarely do we really want a statement about what we would expect to see if we performed the experiment a large number of times. | |
| S Feb 28, 2022 at 17:20 | review | First answers | |||
| Feb 28, 2022 at 17:37 | |||||
| S Feb 28, 2022 at 17:20 | history | answered | benrg | CC BY-SA 4.0 |