## 2 Materials and Methods
### Statistical Methods for Model Validation  
Model validation is the last step in the landslide susceptibility mapping process and is used to assess reliability using statistical methods. It is important to define the accuracy of the model because a landslide susceptibility map without validation is meaningless in the scientific world [46]. In this case statistical method used was the ROC curve, originally developed during World War II to evaluate the capabilities of radar receivers in detecting targets, later also used in the medical field to perform diagnostic tests, and in machine learning [47, 48]. The ROC curve (Receiver Operating Characteristic curve) is a graphical representation for evaluating the performance of a binary classification model that shows the relationship between the sensitivity (or true positive rate) and the specificity (false positive rate) of a test. The points on the ROC curve represent pairs of (false positive, true positive) derived from different contingency tables created by varying the boundary values. In relation to the occurrence of landslides, the sensitivity is calculated as follows:  
\[y-axis,\ sensitivity=(TP/(TP+FN))\]  
\(TP\) = true positive, \(FN\) = false negative, whereas specificity is described by the following formula:  
\[x-axis,\ sensitivity=(FP/(FP+TN))\]  
\(FP\) = false positive, \(TN\) = true negative.  
In this context, true negatives represent the probability that a non-slide area is correctly detected by the LSI (Landslide Susceptibility Index); false positives, represent the probability that a landslide area will not be detected in relation to the LSI. On the other hand, true positives represent the probability that a landslide area is correctly classified in relation to LSI, while false negatives represent the probability that a 'non-landslide area' is incorrectly classified as a 'landslide area' with LSI. ROC curves can be quantitatively summarized using the area under the curve (AUC), measures the model's ability to discriminate between two classes (e.g., landslide and non-landslide) and provides a scale for assessing the overall quality of a model, the larger the AUC, the better the model's performance across the entire range of possible threshold values [49]. The area under the curve can take values between 0.5 and 1.0, the larger the area under the curve (i.e., the closer the curve is to the upper left-hand corner of the graph), the greater the discriminating power of the test. To interpret the values of the area under the ROC curve, one can refer to the following classification [50]:  
* AUC = 0.5 the test is not informative;
* 0.5 < AUC \(\leq\) 0.7 the test is inaccurate;
* 0.7 < AUC \(\leq\) 0.9 the test is moderately accurate;
* 0.9 < AUC < 1.0 the test is highly accurate;
* AUC = 1 perfect test.  
In the present work, 20% of the total landslides used in the calculation of the susceptibility map (training test) were used to validate the susceptibility map (Figure 4).  
Two polygons were created for the validation of landslides:  
* the first file with the original landslide polygons then correctly georeferenced
* a second file with the landslide polygons deliberately shifted to create 'fake' landslide polygons to be used for the AUC calculation; this second file is crucial because a conservative model might detect landslide areas well, but mistake non-landslide areas for landslide areas.