Prediction versus Confidence interval

Forecasting versus predictions

Saying something may happen with 80% probability and sizing your trade against that chance isn't the same as predicting that it will definitely happen. More importantly, those forecasts may not have a long horizon at all, depending on the nature of their forecast.

Prediction intervals

Comparison of measurement methods. In the example, a new spectral method for measuring whole blood hemoglobin is compared with a reference method. But first, let's start with discussing the large difference between a confidence interval and a prediction interval. Prediction interval versus Confidence interval

Very often a confidence interval is misinterpreted as a prediction interval, leading to unrealistic “precise” predictions. As you will see, prediction intervals (PI) resemble confidence intervals (CI), but the width of the PI is by definition larger than the width of the CI.

Let’s assume that we measure the whole blood hemoglobin concentration in a random sample of 100 persons. We obtain the estimated mean (Est_mean), limits of the confidence interval (CI_Lower and CI_Upper) and limits of the prediction interval (PI_Lower and PI_Upper): (The R-code to do this is in the next paragraph)

The graphical presentation:

A Confidence interval (CI) is an interval of good estimates of the unknown true population parameter. About a 95% confidence interval for the mean, we can state that if we would repeat our sampling process infinitely, 95% of the constructed confidence intervals would contain the true population mean. In other words, there is a 95% chance of selecting a sample such that the 95% confidence interval calculated from that sample contains the true population mean.

Interpretation of the 95% confidence interval in our example:

• The values contained in the interval [138g/L to 143g/L] are good estimates of the unknown mean whole blood hemoglobin concentration in the population. In general, if we would repeat our sampling process infinitely, 95% of such constructed confidence intervals would contain the true mean hemoglobin concentration.

A Prediction interval (PI) is an estimate of an interval in which a future observation will fall, with a certain confidence level, given the observations that were already observed. About a 95% prediction interval we can state that if we would repeat our sampling process infinitely, 95% of the constructed prediction intervals would contain the new observation. Interpretation of the 95% prediction interval in the above example:

• Given the observed whole blood hemoglobin concentrations, the whole blood hemoglobin concentration of a new sample will be between 113g/L and 167g/L with a confidence of 95%. In general, if we would repeat our sampling process infinitely, 95% of the such constructed prediction intervals would contain the new hemoglobin concentration measurement.

Remark: Very often we will read the interpretation “The whole blood hemogblobin concentration of a new sample will be between 113g/L and 167g/L with a probability of 95%.” (for example on wikipedia). This interpretation is correct in the theoretical situation where the parameters (true mean and standard deviation) are known. > From <https://www.r-bloggers.com/prediction-interval-the-wider-sister-of-confidence-interval/>