Credible Interval

A credible interval is an interval containing a specified amount of the posterior probability of a parameter in Bayesian analysis. For observed data , a parameter with a continuous posterior distribution, and , a credible interval satisfies

An equal-tail credible interval has endpoints at the and quantiles of the posterior distribution (Gelman et al. 2013, p. 33). For a discrete posterior distribution, an interval containing at least of the posterior probability is used when exact equality is unattainable.

This probability statement conditions on the observed data, the prior distribution, and the likelihood function. A confidence interval instead has a coverage probability defined over repeated samples.