# Credible interval

## Concept in Bayesian statistics / From Wikipedia, the free encyclopedia

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In Bayesian statistics, a **credible interval** is an interval used to characterize a probability distribution. It is defined such that an unobserved parameter value has a particular probability to fall within it. For example, in an experiment that determines the distribution of possible values of the parameter $\mu$, if the probability that $\mu$ lies between 35 and 45 is 0.95, then $35\leq \mu \leq 45$ is a 95% credible interval.

Credible intervals are typically used to characterize posterior probability distributions or predictive probability distributions.^{[1]} The generalisation to multivariate problems is the **credible region**.

Credible intervals are a Bayesian analog to confidence intervals in frequentist statistics.^{[2]} The two concepts arise from different philosophies:^{[3]} 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.