Abstract
The cost-loss decision model is described as a mathematical programming problem where the objective is to derive the maximum economic benefit from a given forecast. The necessary conditions for using a categorical forecast in preference to a climatological forecast are determined. The model is extended to show how a multi-state forecast can be decomposed into a set of two-state forecasts, which can be used to maximize economic benefits. The two-state model is particularly suited to air pollution forecasting where the objective is to prevent the consequences of a severe air pollution episode. The decomposition of a multi-state is illustrated for the bivariate normal distribution where forecast accuracy is measured in terms of the correlation coefficient between predicted and observed values. The criteria developed for measuring forecast effectiveness are applied to air pollution forecasts made in California.
