4.8
4.9
4.7

# Discuss the importance of constructing confidence intervals for the population,Discuss

Discuss the importance of constructing confidence intervals for the population mean.
In, specifically, aprediction intervalis an estimate of anin which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in.
Prediction intervals are used in bothand: a prediction interval bears the same relationship to a future observation that a frequentistor Bayesianbears 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.
For example, if one makes thethat the underlying distribution is a, and has a sample set {X1, ,Xn}, then confidence intervals and credible intervals may be used to estimate theandof the underlying population, while prediction intervals may be used to estimate the value of the next sample variable,Xn+1.
Alternatively, in, 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 about 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,[]following the focus on observables by
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