## 4 Results and Discussion  
### First and Second Step Results and Discussion  
Figure 2 shows the results of the second step, consisting of repeating the first step 10 times on randomized samples and setting EXTCV to 20%, performing a Monte Carlo estimation of the selection algorithms on randomized samples. The results are expressed as FNR and FPR in percent. Figure 3 shows the bar plot of the mean values of the FNR and FPR of Figure 2 and their standard deviation of the mean (bar). Furthermore, the PLS-0-0 model (i.e., raw spectra  
Figure 2: Boxplot of results of the second step, consisting of repeating the first step 10 times on randomized samples and setting EXTCV to 20%. Results are expressed as FNR and FPR in percent. The red “+” represent the data outliers. without any derivative) is statistically estimated to have an FNR of 0% in all 10 randomized replicates. The red arrow in Figure 3 indicates the optimal model with regard to FNR (i.e., the consumer risk). Figure 4 shows a replicate of the PLS-0-0 model, belonging to the first step. It is to be highlighted that the algorithm does not know the EXTCV; all the plots regarding the EXTCV are only for informative purposes. The categorical nature of the model is shown by the FPR and FNR values appearing in one of the plots in Figure 4.  
Figure 4: Replicate of PLS-0-0 model. It is to be highlighted that the algorithm does not know the EXTCV; all plots regarding the EXTCV are only for informative purposes. The categorical nature of the model is shown by the FPR and FNR values appearing in one of the plots. Figure 3: Bar plot, as mean and standard deviation of mean, of results of the second step, consisting of repeating the first step 10 times on randomized samples and setting EXTCV to 20%. Results are expressed as FNR and FPR in percent. Red arrow indicates optimal model with regard to FNR (i.e., consumer risk). The first step allowed comparison of the performance of the different M-D-OPTN models under test. To this aim, Figure 5 shows, from the same replicate previously considered, the boxplot of performances expressed as RANGEPER%@95%. Finally, the goodness of the overall underlying statistics must be assessed. Figure 6a allows to evaluate this aspect. Indeed, Figure 6a shows, for the considered replicate, the relationship between the RPD and R2 CV for all the runs performed, all the considered models (PCR, PLS), and all the grouped Monte Carlo evaluations (where the standard deviation of the mean of each group is shown). Figure 5: Boxplot graphs of a replicate of the first step, allowing the comparison of the performance of the M-D-OPTN models under evaluation. Model performance is expressed as RANGEPER%@95%. Each replicate was performed using 50 Monte Carlo runs in its final evaluation, once maximum RPD and the subset of the optimal wavelengths were identified. Figure 6: **(a)** Relationship between RPD and R2 CV, for considered replicates, for all runs performed, for all considered models (PCR, PLS) and all grouped Monte Carlo runs. **(b)** Relationship between RANGEPER%@95% and RPD. Correlation is hyperbolic; RPD is inversely correlated with RANGEPER%@95%. According to [53; 54], the relation is 1/sqrt (1-R2 CV); therefore, RPD and R2 CV are two transposable parameters, but RPD is more discriminant than R2 CV [53]. To this aim, it is normally accepted that a prediction model can be used in quality control when RPD \(\geq\) 5.0 and to quantitatively measure the property of interest when RPD \(\geq\) 8.1 [50; 55]. However, there is no definite accord among various authors as the RPD parameter does not allow the model's statistical reliability to be evaluated in terms of the statistically guaranteed maximum measurement error on unknown samples, this last being the value needed by the final user of the model to quantify its measuring reliability. Indeed, because any statistical model is used to forecast the property of interest on unknown samples, a prediction model must provide its error rate with a guaranteed significance level.