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Uncertainty and models

Prediction-interval chart

Shows a predicted value with an interval for an individual future outcome.

  • Plot
  • Uncertainty
  • Forecasting

What it answers

What range may contain an individual future outcome?

Shape
Prediction line and outcome band
What it shows
Predictive uncertainty and changing spread.

Example

The question

What range of sales should we plan for next quarter?

Weekly sales with forecast and 80% prediction interval (EUR thousand)

Weekly sales with forecast and 80% prediction interval (EUR thousand)Actual sales for weeks 1 to 14, then a dashed forecast to week 20 with a pink band where 8 in 10 future weeks should fall. The band widens from about ±10 to ±20 thousand.ActualForecastEUR thousand per week6080100120140160W1W3W5W7W9W11W13W15W17W19
Weekly sales with forecast and 80% prediction interval (EUR thousand)Actual sales for weeks 1 to 14, then a dashed forecast to week 20 with a pink band where 8 in 10 future weeks should fall. The band widens from about ±10 to ±20 thousand.ActualForecastEUR thousand per week6080100120140160W1W5W9W13W17
Actual sales for weeks 1 to 14, then a dashed forecast to week 20 with a pink band where 8 in 10 future weeks should fall. The band widens from about ±10 to ±20 thousand.

Illustrative data. It belongs to no company.

When to use it

Use it when

Forecasting outcomes with an appropriate predictive model.

Avoid it when

When coverage assumptions are unknown or bands are treated as guarantees.

How to read it

Read predicted value and labelled coverage bounds.

Note

State coverage and prediction target.

The data you need

Layout
Wide interval summary
Fields
X or Time: number/date; Estimate,Lower,Upper: numbers
One row is
One ordered curve position and its estimate and bounds. What is the grain?
Rules
Sort X/time, pair all bounds and specify interval meaning and coverage. Compute intervals using an appropriate model.
Optional
Alternative Estimate,LowerError,UpperError distances. Distinguish bounds from distances.
Preparation
Fit or obtain a suitable model/estimate first, then pair estimates with correctly labelled bounds or standard errors. Preserve coverage and scale information.
Units
Estimates and interval endpoints share an effect/measurement unit unless transformed. Coverage such as 95% is a model-based probability statement, not a data-share denominator.
Example of the input layout: Wide interval summaryA wide table: one row per item, with a separate column for each measure or period.X or TimeEstimateLowerUpper…ABC
A wide table: one row per item, with a separate column for each measure or period.

Worked example

Prediction 10 with 95% prediction interval 4-16. It is wider than a supplied mean-confidence interval 8-12 because individual variability is included.

XEstimateLowerUpper
110812
212915
3141018
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