Bayesian estimation | Statistical intervals

Credible interval

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 and confidence regions 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 , if the subjective probability that lies between 35 and 45 is 0.95, then is a 95% credible interval. (Wikipedia).

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Related pages

Sufficient statistic | Scale parameter | Confidence region | Mode (statistics) | Parameter | Markov chain Monte Carlo | Confidence interval | Bayesian statistics | Decision theory | Nuisance parameter | Location parameter | Probability