The cost of uncertainty: quality-value relationships for yes/no forecasts in the signal detection model
Ian Mason
32 Hensman St Latham ACT 2615 Australia
This note investigates the relationship between the skill and value of forecasts using a modeling approach based on signal detection theory (SDT).
The economic value of weather forecasts in a 2-action, 2-state decision situation can be modeled as a function of forecasting skill, decision threshold, climate and the economic parameters of the decision situation.
In general the value of forecasts increases monotonically with increasing skill, measured by the SDT d' parameter . In some circumstances, however, reversal of the expected relationship between forecasting skill and economic value is found, so that forecast value decreases as skill increases. This is associated with use of sub-optimal decision thresholds.
Thresholds on skill are found for some decision situations, such that forecasts of lower quality have no economic value even though they have some positive skill and are applied optimally.
These results reinforce the importance of using the optimal decision threshold in realizing the full potential value of the forecasts.