A statement about the likely value of a future observation. It has a similar interpretation to a confidence interval but the interval is wider because it allows for the random error associated with the future observation.
For example, if a random sample of n observations is taken from a population with known variance σ2 and unknown mean μ, then the natural estimate of μ is x̄, the sample mean. A confidence interval for μ is based on the uncertainty in the estimate, which has variance σ2/n. However, associated with a future observation from this distribution is the future random sampling variation with variance σ2. A prediction interval for a future observation is based on the sum of the two variances, σ2+σ2/n.
Subjects: Probability and Statistics.