Credible interval | Wikipedia audio article

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00:00:14 1 Choosing a credible interval
00:00:29 2 Contrasts with confidence interval






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SUMMARY

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In Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution. 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 distribution of possible values of the parameter



μ


{\displaystyle \mu }
, if the subjective probability that



μ


{\displaystyle \mu }
lies between 35 and 45 is 0.95, then



35
≤
μ
≤
45


{\displaystyle 35\leq \mu \leq 45}
is a 95% credible interval.

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