Scoring epidemiological forecasts on transformed scales
Fig 6
Mean WIS in different locations for different transformations applied before scoring.
Locations are sorted according to the mean observed value in that location. Shown are scores for two-week-ahead forecasts of the EuroCOVIDhub-ensemble. On the natural scale (with no transformation prior to applying the WIS), scores correlate strongly with the average number of observed values in a given location. The same is true for scores obtained after applying a square-root transformation, or after applying a log-transformation with a large offset a. For illustrative purposes, a was chosen to be 101630 for cases and 530 for deaths, 10 times the respective median observed value. For large values of a, log(x + a) grows roughly linearly in x, meaning that we expect to observe the same patterns as in the case with no transformation. For decreasing values of a, we give more relative weight to scores in small locations.