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    $\begingroup$ The confidence interval is the answer to the question "give me an interval that will bracket the true value of the statistic with probability p if the experiment is repeated a large number of times". The credible interval is an answer to the question "give me an interval that brackets the true value with probability p". First of all, the statement regarding a frequentist interpretation of probability leaves something to be desired. Perhaps, the issue lies in the use of the word probability in that sentence. Second, I find the credible interval "definition" to be a little too simplistic... $\endgroup$ Commented Apr 14, 2012 at 17:38
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    $\begingroup$ ...and slightly misleading considering the characterization you give to a CI. In a related vein, the closing sentence has the same issue: If you want an interval that contains the true value 95% of the time, then choose a credible interval, not a confidence interval. The colloquial use of "contains the true value 95% of the time" is a bit imprecise and leaves the wrong impression. Indeed, I can make a convincing argument (I believe) that such wording is much closer to being the definition of a CI. $\endgroup$ Commented Apr 14, 2012 at 17:42
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    $\begingroup$ Request: It would be helpful for the downvoter to this answer to express their opinion/reasons in the comments. While this question is a bit more likely than most to lead to extended discussion, it is still useful to provide constructive feedback to answerers; that is one of the easiest ways to help improve the overall content of the site. Cheers. $\endgroup$ Commented Apr 14, 2012 at 19:06
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    $\begingroup$ Dikran, yes, I agree. That was part of what I was trying to draw out a little bit more in the edits. A radical frequentist (which I am certainly not) might state it provocatively as: "A CI is conservative in that I design the interval beforehand such that no matter what particular data I happen to observe, the parameter will be captured in the interval 95% of the time. A credible interval arises from saying 'Oops, someone just threw some data in my lap. What's the probability the interval I construct from that data contains the true parameter?'" That is a bit unfair in the latter case... $\endgroup$ Commented Apr 14, 2012 at 20:20
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    $\begingroup$ So, I just looked at that Example 5 in the Jaynes paper for the first time. My immediate reaction upon seeing the definition of $\theta^\star$ was: That's not based on the sufficient statistic! I was relieved to at least see that this wasn't the totality of Jaynes argument, but it's a pretty weak example in this instance. It's similar to another one I saw in a related question here where a poster makes a quite flawed argument by constructing an infinite CI and then argues (essentially) that it's a silly thing to do. In both cases, it's a strawman at the least and disingenuous at worst. $\endgroup$ Commented Apr 14, 2012 at 20:52