Okay, so, credible intervals aren't the same as confidence intervals. We all know that. In fact, they're only guaranteed to be the same when they're about a location or a scale parametre with a noninformative prior when they can be calculated from a single sufficient statistic. Furthermore, the most obvious way in which they differ is exactly in the prior, since if you have an informative prior then the credible interval even for the mean of a normal distribution will be different than the confidence one.
However, is there a simple example of a continuous case where they differ even with noninformative priors, that's not Jaynes' Truncated Exponential?
Googling finds the truncated exponential, also the other time this question was answered here but that's discrete and not terribly clear either.
So, what I want is some example of a continuous variable that's reasonably simple (by reasonably simple I mean "doesn't need obscure theorems like the characteristic function theorem") where the prior is noninformative and confidence and credible intervals do not coincide.
I wonder why people marked this question as a duplicate of another question when I explicitly linked to that other question and said that it did not answer my question, and therefore those were not the answers I was looking for. Specifically because they were either too complex or too discrete.