from the first act of “Sant’Alessio” (1631) by Stefano Landi (1587–1639), text by Giulio Rospigliosi (1600–69, also known as Pope Clemente IX).
“Pazzo è bene da catene, Chi fastidio mai si dà Per saper quel che sarà … ”
He is a raving madman who ever takes the trouble to know what the future holds …
First of all, the author wants to thank AMS for granting a full-cost waiver for this manuscript. Thanks to Rich Caruana (Cornell University) for introducing the author to the bagging/ensemble technique during the AMS Short Course on Artificial Intelligence Applications to Environmental Science (Atlanta, GA, 28–29 January 2006) organized by Professor Caren Marzban, whose help never left the author. The author wants to thank also the “hail volunteers,” who managed for free the hailpad stations and Rich Rotunno (NCAR) for improvements to the English in this paper. Last but not least, he thanks the “GNU generation” for having provided such good—and free—tools such as R, Python, LaTeX, Emacs, as well as Linux itself.
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Radar and lightning data have not been investigated here because their database record is too short with respect to that of the hailpads and because the focus is on short-term forecasting and not nowcasting.
For this first experiment only the sounding-derived data computed with the Tv method are used.
Note that a 10–I 4–H NN already has 49 free parameters (adaptive weights) to be set, while a 10–I 2–H NN has only 25 weights.
A similar effect has been found by Manzato (2007a, his Fig. 11) on the PSS metric, when evaluating different thresholds of accumulated rain.
PSS was used instead of CEE because the ensemble classifier has a binary output, while CEE can be computed only from the continuous forecasts in the 0 < y < 1 range.
The ROC curve was developed, before the Swets paper, during the Second World War, by engineers working on the analysis of radar signals. Kleiber (2008) recognizes the ROC curve as a variant of the Lorenz curve, first published in 1905 by the economist Max Otto Lorenz (Lorenz 1905).
It should be said that these correlations are both very low from a practical point of view, even if they are statistically significant, since the p value is <2 × 10−5 and <2 × 10−16, respectively.
In the regression problem, BIAS means the average forecast minus the average observation and should not be confused with the frequency BIAS used in the classification problem.