Credible intervals

In Bayesian statistics, a credible interval is an interval in the domain of a posterior probability distribution or predictive distribution used for interval estimation. The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals in frequentist statistics, although they differ on a philosophical basis; Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value. Also, Bayesian credible intervals use (and indeed, require) knowledge of the situation-specific prior distribution, while the frequentist confidence intervals do not.

For example, in an experiment that determines the uncertainty distribution of parameter ${\displaystyle \mu }$, if the probability that ${\displaystyle \mu }$ lies between 35 and 45 is 0.95, then ${\displaystyle 35\leq \mu \leq 45}$ is a 95% credible interval.

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