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Keywords:

  • Calibration;
  • Coherent combination formula;
  • Forecast aggregation;
  • Linear opinion pool;
  • Model averaging;
  • Probability forecasting;
  • Reliability;
  • Resolution;
  • Sharpness

Summary.  Linear pooling is by far the most popular method for combining probability forecasts. However, any non-trivial 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. Towards this end, we propose a beta-transformed linear opinion pool for the aggregation of probability forecasts from distinct, calibrated or uncalibrated sources. The method fits an optimal non-linearly 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.