<P> Confidence intervals are one method of interval estimation, and the most widely used in frequentist statistics . An analogous concept in Bayesian statistics is credible intervals, while an alternative frequentist method is that of prediction intervals which, rather than estimating parameters, estimate the outcome of future samples . For other approaches to expressing uncertainty using intervals, see interval estimation . </P> <P> A prediction interval for a random variable is defined similarly to a confidence interval for a statistical parameter . Consider an additional random variable Y which may or may not be statistically dependent on the random sample X . Then (u (X), v (X)) provides a prediction interval for the as - yet - to - be observed value y of Y if </P> <Dl> <Dd> Pr θ, φ (u (X) <Y <v (X)) = γ for all (θ, φ). (\ displaystyle (\ Pr) _ (\ theta, \ varphi) (u (X) <Y <v (X)) = \ gamma (\ text (for all)) (\ theta, \ varphi). \,) </Dd> </Dl> <Dd> Pr θ, φ (u (X) <Y <v (X)) = γ for all (θ, φ). (\ displaystyle (\ Pr) _ (\ theta, \ varphi) (u (X) <Y <v (X)) = \ gamma (\ text (for all)) (\ theta, \ varphi). \,) </Dd>

Who determines the level of confidence for an interval estimate