I am wondering if prediction interval and credible interval evaluate the same thing.
For instance with a linear regression, when you estimate the prediction interval of a fitted values, you estimate the $(1-\alpha)\%$ limits of the interval in which you expect your value to fall. Conversely to a confidence interval, you do not focus on a distribution parameter such as the mean value, but on the value that your explained variable could take for a given X value (supposing that $\ Y = a + b.X$).
When you estimate the fitted value for a given $X$ value within a Bayesian framework, from the posterior probability distribution, you can estimate a credible interval. Does this interval give you the same information on the fitted value or not?