## 3 Results  
### Statistical Model  
As stated in Section 2.1.1, the proposed procedure is based on the distinction between terrain computational units related to the spatial resolution of the map, _TCU_, and terrain zoning units related to the desired informative resolution of the zoning, _TZU_. The variables employed within the model have been expressed in raster format using 107,513 square grid cells for Vaglio Basilicata and 64,441 square grid cells for Trivigno as _TCU_, whose single size is equal to 20 \(\times\) 20 m. The dichotomous dependent variable is derived from the official inventory map developed by the Interregional River Basin Authority of Basilicata region, reporting 157 slow-moving landslides for Vaglio Basilicata (21,420 _TCUs_ covered) and 724 for Trivigno (32859 _TCUs_ covered). The following ten independent variables are used in the analysis (Tables 3 and 4): distance from roads (V1); distance from river network (V2); slope (V3); terrain ruggedness index (V4); topographic position index (V5); aspect (V6); plan curvature (V7); flow accumulation (V8); topographic index (V9); and stream power index (V10). All independent variables are numeric variables: eight of them (slope, terrain ruggedness index, topographic position index, aspect, plan curvature, flow accumulation, topographic index, stream power index) are derived from the available digital elevation model, and the remaining two (distance from river network, distance from roads) are derived from categorical vector maps. All variables were classified using a quantile criterion with eight classes, i.e., each class includes about 12.5% of the total population (Tables 3 and 4). Bivariate analyses were carried out using the SZ plugin developed by [PERSON] et al. [46]. The plugin is a collection of processing scripts in Python which run as part of the QGIS platform. Among the available statistical approaches, the weight of evidence (_WoE_) method was used. The _WoE_ allows to quantify how prone an event occurrence is according to the proportion of presence/absence for each class of the independent variables. Two weights are assigned for each class: \(W_{i}^{+}\) and \(W_{i}^{-}\). The weights represent, respectively, the positive and negative influence of the independent variables on a potential landslide. They are calculated by the following equations:  
\[W_{i}^{+}=ln\ \frac{\frac{M_{1}}{M_{1}+M_{2}^{2}}}{\frac{M_{3}}{M_{3}+M_{4}}} \tag{2}\]  
\[W_{i}^{-}=ln\ \frac{\frac{M_{2}}{M_{1}+M_{2}^{2}}}{\frac{M_{4}}{M_{3}+M_{4}}} \tag{3}\]  
\[W_{i}=W_{i}^{+}-W_{i}^{-} \tag{4}\]  
where \(M_{1}\) is the number of _TCUs_ where both the variable class and the event are present; \(M_{2}\) is the number of _TCUs_ where the variable class is absent, while the event is present; \(M_{3}\) is the number of _TCUs_ where the variable is present, while the event is absent; and \(M_{4}\) is the number of _TCUs_ where both the variable class and the event are absent. The weight contrast, \(W_{i}\), is the final weight assigned to each class of the variable. It evaluates the relation between the spatial distribution of the causes (i.e., the independent variables) and the spatial distribution of the events (i.e., the landslides). Tables 5 and 6 report the values of the statistical weights computed for Vaglio Basilicata and Trivigno, using Equation (4), for each class of each independent variable \(Vi\). The following main comments arise from the values reported in the table. The overall maximum weight is attributed to class 8 of variable V8 at Vaglio Basilicata (\(\text{W}_{88}^{V}=1.12\)) and to class 8 of variable V10 at Trivigno (\(W_{108}^{T}=1.05\)). High values of weights are computed for a number of classes for variables V7, V9 and V10 at Vaglio Basilicata (\(W_{78}^{V}=0.54\), \(W_{98}^{V}=0.89\), \(W_{108}^{V}=0.99\)) and for variables V2, V7 and V8 at Trivigno (\(W_{24}^{T}=0.68\), \(W_{78}^{T}=0.89\), \(W_{88}^{T}=0.88\)). At Vaglio Basilicata, out of the eight classes of variable V1, only class 8 assumes a positive weight value (\(W_{18}^{V}=0.49\)).