A number of recent papers have assessed the economic value of ensemble-based weather or climate forecasts, particularly using the cost-loss decision-making model. In such studies, it is generally assumed that the probability forecasts are produced by taking the ensembles at "face value"; that is, by the relatively frequency of occurrence of the event among the limited number of ensembles. In effect, the decision maker ignores the uncertainty in estimating the probability in this manner. But the principles of Bayesian inference and prediction provide a natural mechanism to incorporate such uncertainty into the decision process.

The naive approach of taking the ensembles at face value corresponds to a Bayesian analysis with a prior distribution on the forecast probability that places most of the weight on probabilities near zero or one (i.e., only appropriate if it were believed that the forecasts were near perfect). The "fictitious ensemble" approach, in which an extra ensemble is imagined so as to avoid probability forecasts of zero or one, corresponds to a Bayesian analysis with a prior distribution still only appropriate if it were believed that the forecasting system were highly skillful.

For more plausible forms of prior distribution on the forecast probability (e.g., uniform distribution or informative prior with mode near the climatological probability), a Bayesian analysis is performed. Whether in terms of reliability (or "calibration"), skill (e.g., Brier score), or economic value (i.e., for cost-loss decision-making model), the apparent effects of ensemble size on forecasting performance are smaller than those previously obtained on the basis of the naive/face value approach.