Timeline for What's the difference between a confidence interval and a credible interval?
Current License: CC BY-SA 3.0
16 events
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| Oct 19, 2020 at 14:23 | comment | added | Albert Chen | One thing confuses me, can someone help me. The frequentist example CI is about random variable "chips". The Bayesian example CI is about "jar". How can you mix these two separate concepts? My confusion is in the frequentist statement here: if the number of chips on the cookie I draw is 1, my confidence interval will be {B,C,D}. If the cookie is known to be 1, which is not a random, you can tell for sure it is in the CI or not, why random statement (i.e. there's no longer a CI)? | |
| Sep 23, 2014 at 7:07 | comment | added | Garrett |
The author says "you will expect 80 of the robots to get the wrong answer, each having >73% belief in its incorrect conclusion!", but this should have been >72% belief, since 72% is the minimum credibility in the credibility intervals table.
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| Sep 23, 2014 at 7:03 | comment | added | Garrett |
@BYS2, when the author says that "What if the true value is, say, 0.37? If it is, then your method, run start to finish, will be WRONG 75% of the time", they are just giving example numbers they made up. In this particular case, they would be referring to some prior distribution that had a very low value at 0.37, with most of its probability density elsewhere. And we assume that our example distribution would perform very poorly when the true value of the parameter happens to be 0.37, similarly to how Bayesia's credibility intervals failed miserably when the jar happened to be type-B.
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| Nov 18, 2012 at 21:29 | history | edited | Keith Winstein | CC BY-SA 3.0 |
added 250 characters in body
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| Nov 14, 2012 at 19:41 | comment | added | RobertF | Cool illustration! How would the chocolate chip model confidence & credibility intervals be adjusted if we're allowed to sample n cookies from the jar? And can we rate the accuracy of the two approaches as we accumulate data on relative freq. of jars that are delivered? I'll guess the Bayesian approach will make better predictions once we're fairly certain about the prior distribution (say after ~30 deliveries?). But if the prior dbn were to abruptly change (say a new deliveryman takes the job) then the Frequentist approach would have the advantage. | |
| Nov 11, 2012 at 18:37 | history | edited | Keith Winstein | CC BY-SA 3.0 |
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| Nov 9, 2012 at 22:53 | history | edited | Keith Winstein | CC BY-SA 3.0 |
Made example more compelling
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| Jul 6, 2012 at 11:18 | comment | added | BYS2 | sorry to revive this super old post but a quick question, in your post in the section where the frequentist criticizes the Bayesian approach you say: "What if the true value is, say, 0.37? If it is, then your method, run start to finish, will be WRONG 75% of the time." How did you get those numbers? how does 0.37 correspond to 75% wrong? Is this off of some type of probability curve? Thanks | |
| Feb 5, 2011 at 11:38 | comment | added | probabilityislogic | ...cont'd... but it is much more convenient to just write $p(\theta)$, with the understanding of what it means "in the background". Clearly this can cause much confusion. | |
| Feb 5, 2011 at 11:34 | comment | added | probabilityislogic | Good answer - just one minor point, you say "....Instead of saying the parameter has one true value, a Bayesian method says the value is chosen from some probability distribution....." This is not true. A Bayesian fits the probability distribution to express the uncertainty about the true, unknown, fixed value. This says which values are plausible, given what was known before observing the data. The actual probability statement is $Pr[\theta_0\in (\theta,\theta+d\theta)|I]$, where $\theta_0$ is the true value, and $\theta$ the hypothesised one, based on information $I$. | |
| Sep 8, 2010 at 20:27 | vote | accept | Matt Parker | ||
| Sep 8, 2010 at 16:58 | history | bounty ended | Matt Parker | ||
| Sep 4, 2010 at 5:28 | history | edited | Keith Winstein | CC BY-SA 2.5 |
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| Sep 4, 2010 at 5:22 | history | edited | Keith Winstein | CC BY-SA 2.5 |
Added extended cookie-jar example
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| Sep 1, 2010 at 21:35 | history | edited | Keith Winstein | CC BY-SA 2.5 |
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| Sep 1, 2010 at 18:46 | history | answered | Keith Winstein | CC BY-SA 2.5 |