Probabilities, Odds, and Forecasts of Rare Events

Abstract

Several issues related to the mode of expression of forecasts of rare events (RSEs) are addressed in this paper. These issues include the correspondence between forecasters' judgments and their forecasts, the problem of overforecasting, and the use of forecasts as a basis for rational decision making. Neither forecasters nor users are well served by current practices, according to which operational forecasts of RSEs are generally expressed in a categorical format. It is argued here that sound scientific and economic reasons exist for expressing forecasts of RSEs in terms of probabilities. Although quantification of uncertainty in forecasts of RSEs?-and the communication of such information to users?-presents some special problems, evidence accumulated from a multitude of operational and experimental probabilistic weather forecasting programs suggests that these problems involve no insurmountable difficulties. Moreover, when a probabilistic format is employed, forecasts of RSEs can correspond to forecasters? true judgments, the forecasting and decision-making tasks can be disentangled, the rationale for overforecasting RSEs is eliminated, and the needs of all users can be met in an optimal manner. Since the probabilities of RSEs seldom achieve high values, it might be desirable to provide users with information concerning the likelihood of such events relative to their climatological likelihood. Alternatively, the relative odds?-that is, the ratio of an event's forecast odds to its climatological odds?-could be reported. This supplemental information should help to focus users? attention on those occasions on which the probability of RSEs is relatively high.