Combining Probability Forecasts

Linear pooling is by the far the most popular method for combining probability forecasts. However, any nontrivial weighted average of two or more distinct, calibrated probability forecasts is necessarily uncalibrated and lacks sharpness. In view of this, linear pooling requires recalibration, even in the ideal case in which the individual forecasts are calibrated. Toward this end, we propose a beta transformed linear opinion pool (BLP) for the aggregation of probability forecasts from distinct, calibrated or uncalibrated sources. The BLP method fits an optimal nonlinearly recalibrated forecast combination, by compositing a beta transform and the traditional linear opinion pool. The technique is illustrated in a simulation example and in a case study on statistical and National Weather Service probability of precipitation forecasts.