information:classification, quality:corruption, structural:expansion
Contrasts with confidence interval

A frequentist 95% confidence interval means that with a large number of repeated samples, 95% of such calculated confidence intervals would include the true value of the parameter. In frequentist terms, the parameter is fixed (cannot be considered to have a distribution of possible values) and the confidence interval is random (as it depends on the random sample).

Bayesian credible intervals differ from frequentist confidence intervals by two major aspects:

For the case of a single parameter and data that can be summarised in a single sufficient statistic, it can be shown that the credible interval and the confidence interval coincide if the unknown parameter is a location parameter (i.e. the forward probability function has the form P r (x | μ) = f (x − μ) {\displaystyle \mathrm {Pr} (x|\mu)=f(x-\mu)}), with a prior that is a uniform flat distribution; and also if the unknown parameter is a scale parameter (i.e. the forward probability function has the form P r (x | s) = f (x / s) {\displaystyle \mathrm {Pr} (x|s)=f(x/s)}), with a Jeffreys' prior P r (s | I) ∝ 1 / s {\displaystyle \mathrm {Pr} (s|I)\;\propto \;1/s} — the latter following because taking the logarithm of such a scale parameter turns it into a location parameter with a uniform distribution.But these are distinctly special (albeit important) cases; in general no such equivalence can be made.