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.

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