Prediction interval

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In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.

A simple example is given by a six-sided die with face values ranging from 1 to 6. The confidence interval for the estimated expected value of the face value will be around 3.5 and will become narrower with a larger sample size. However, the prediction interval for the next roll will approximately range from 1 to 6, even with any number of samples seen so far.

Prediction intervals are used in both frequentist statistics and Bayesian statistics: a prediction interval bears the same relationship to a future observation that a frequentist confidence interval or Bayesian credible interval bears to an unobservable population parameter: prediction intervals predict the distribution of individual future points, whereas confidence intervals and credible intervals of parameters predict the distribution of estimates of the true population mean or other quantity of interest that cannot be observed.