Introduction
For example, if one makes the parametric assumption that the underlying distribution is a normal distribution, and has a sample set {X1, ..., Xn}, then confidence intervals and credible intervals may be used to estimate the population mean μ and population standard deviation σ of the underlying population, while prediction intervals may be used to estimate the value of the next sample variable, Xn+1.
Alternatively, in Bayesian terms, a prediction interval can be described as a credible interval for the variable itself, rather than for a parameter of the distribution thereof.
The concept of prediction intervals need not be restricted to inference just a single future sample value but can be extended to more complicated cases. For example, in the context of river flooding where analyses are often based on annual values of the largest flow within the year, there may be interest in making inferences about the largest flood likely to be experienced within the next 50 years.
Since prediction intervals are only concerned with past and future observations, rather than unobservable population parameters, they are advocated as a better method than confidence intervals by some statisticians, such as Seymour Geisser, following the focus on observables by Bruno de Finetti.
Read more about this topic: Prediction Interval
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