Credible interval

In <a href="/facts/Bayesian_statistics/9w7b1Bw4">Bayesian statistics</a>, a credible interval is an <a href="/facts/Interval_(statistics)/7G6VxM7I">interval</a> used to characterize a <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a>. It is defined such that an unobserved <a href="/facts/Parameter/zFvVFMv9">parameter</a> value has a particular <a href="/facts/Probability/fgYvMhwb">probability</a> 
 
 
 
 γ
 
 
 {\displaystyle \gamma }
 
 to fall within it. For example, in an experiment that determines the distribution of possible values of the parameter 
 
 
 
 μ
 
 
 {\displaystyle \mu }
 
, if the probability that 
 
 
 
 μ
 
 
 {\displaystyle \mu }
 
 lies between 35 and 45 is 
 
 
 
 γ
 =
 0.95
 
 
 {\displaystyle \gamma =0.95}
 
, then 
 
 
 
 35
 ≤
 μ
 ≤
 45
 
 
 {\displaystyle 35\leq \mu \leq 45}
 
 is a 95% credible interval.
Credible intervals are typically used to characterize <a href="/facts/Posterior_probability/fojsMD0D">posterior probability</a> distributions or <a href="/facts/Predictive_probability_of_success/xhKc6wDn">predictive probability</a> distributions. Their generalization to disconnected or multivariate sets is called credible set or credible region. 
Credible intervals are a <a href="/facts/Bayesian_statistics/9w7b1Bw4">Bayesian</a> analog to <a href="/facts/Confidence_interval/NS8mG5UE">confidence intervals</a> in <a href="/facts/Frequentist_statistics/UcNgebQc">frequentist statistics</a>. The two concepts arise from different philosophies: 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 <a href="/facts/Prior_distribution/JQKAD4o0">prior distribution</a>, while the frequentist confidence intervals do not.

Credible interval open-in-new

Credible interval