Confidence and prediction bands

A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data.

Similarly, a prediction band is used to represent the uncertainty about the value of a new data-point on the curve, but subject to noise.

Confidence and prediction bands are often used as part of the graphical presentation of results of a regression analysis.

If x is measured at the precision of a single year, we can construct a separate 95% confidence interval for each age.

In the definition of a pointwise confidence band, that universal quantifier moves outside the probability function.

[2] In the case of a simple regression involving a single independent variable, results can be presented in the form of a plot showing the estimated regression line along with either point-wise or simultaneous confidence bands.

Confidence bands can be constructed around estimates of the empirical distribution function.

Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.

[3] Confidence bands arise whenever a statistical analysis focuses on estimating a function.

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.