Prediction interval

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

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. Prediction intervals are also present in forecasts. It is difficult to estimate the prediction intervals of forecasts that have contrary series.

Introduction

For example, if one makes the parametric assumption that the underlying distribution is a normal distribution, and has a sample set {X₁, ..., X_n}, 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, X_n+1.