Improving probabilistic infectious disease forecasting through coherence
Fig 3
Graphical example of how mean squared error (MSE) can decrease while skill gets worse for two region example.
A: Purple histograms represent the 10,000 realizations of , while green histograms are the corresponding
. The purple and green points illustrate a particular example of the projection matrix forecasting process. The solid vertical lines denote the true value for each region. B: Top panel shows distribution of MSE for
minus corresponding MSE for
. MSE for
is greater than the MSE for
for all realizations. B: Bottom panel shows single-bin skill score for
minus skill score for
. The incoherent
forecasts are better or equal to the skill for the coherent forecasts for all iterations, with an average improvement greater than 0. This shows the the MSE of the coherent forecasts has decreased (since the difference between the original and projected is positive) and the forecast skill has decreased (since the difference between the original and projected is again positive). Since a decrease in MSE means an improvement and a decrease in forecast skill means a lack of improvement, we see that coherence can have opposite effects on the two scores.