Prediction Bands
Prediction bands are related to prediction intervals in the same way that confidence bands are related to confidence intervals. Prediction bands commonly arise in regression analysis. The goal of a prediction band is to cover with a prescribed probability the values of one or more future observations from the same population from which a given data set was sampled. Just as prediction intervals are wider than confidence intervals, prediction bands will be wider than confidence bands.
In mathematical terms, a prediction band with coverage probability 1−α satisfies the following condition for each value of x:
where y* is an observation taken from the data-generating process at the given point x that is independent of the data used to construct the point estimate and the confidence interval w(x). This is a pointwise prediction interval. It would be possible to construct a simultaneous interval for a finite number of independent observations using, for example, the Bonferroni method to widen the interval by an appropriate amount.
Read more about this topic: Confidence Band
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