Confidence and Prediction Intervals
- Ch. 3 Shmueli, Galit, and Kenneth C. Lichtendahl. Practical Time Series Forecasting with R: A Hands-on Guide. Second edition. Erscheinungsort nicht ermittelbar: Axelrod Schnall Publishers, 2018.
- 5.5 and 7.6 of https://otexts.com/fpp3/forecasting-regression.html 1
Also available in print form: Hyndman, Rob J., and George Athanasopoulos. Forecasting: Principles and Practice. Third print edition. Melbourne, Australia: Otexts, Online Open-Access Textbooks, 2021. https://otexts.com/fpp3/#.
Introduction
This lecture provides the reader with a general understanding of how to use statistical intervals as decision rules. It explains the different techniques used including confidence intervals, prediction intervals, tolerance intervals and control charts.
In environmental monitoring, these intervals are used to compare new observation values with a standard or background value. For example, suppose that a mechanical workshop applies to refinance the mortgage on the workshop, in such cases it is common to require a soil analysis for pollutants such as sulphuric acid 2. If the new measurements are greater than background values, is this evidence of an actual difference, or is it just noise?
To make an objective decision, we create a decision rule based on an interval. If the new values fall outside of the background interval, it suggests potential contamination. If the new values stay within the interval, there is insufficient evidence to suggest the higher measurements aren't caused by chance.
Footnotes
The electrolyte in lead-acid batteries used in modern cars (even in some electric cars to provide 12v to accessories)