## 4 Experimental Results
### Use Different Mathematical Models to Obtain Prediction Patterns from Likelihood Ratios  
The empirical likelihood ratios represent the spatial relationships within the database. They were obtained using the trigger zones distribution image of the 70 active landslides, **70 at**, as DSP, and the ratio transformed images of the three categorical and the five continuous-field maps, **ulpACDIS**, as ISPs. Each model was applied to generate a different prediction pattern. The models integrated the ratios for each ISP. The patterns, displayed in Figure 3, were generated by the five mathematical models each requiring different assumptions and providing incompatible scores computed from identical inputs of likelihood ratios. To identify the patterns and their inputs in the computations, a sequence of short names was used as follows: MODEL_DSP_ISPs, as **FZ_70 at_ulpACDIS** to **BP_70 at_ulpACDIS**. The one-letter ISP abbreviations were used in analyses with subsets of them. \begin{table}
\begin{tabular}{l l} \hline \multicolumn{2}{c}{**Supporting Categorical Units or Classes Converted to ISPs for DSP 70 at**} \\ \hline Land use \(\mathbf{u}_{1-23}\) & \(\mathbf{u}_{2}\), Rock and scree vegetation; \(\mathbf{u}_{3}\), Bedrock outcrops and \\  & surficial deposits. \\ \hline \multirow{4}{*}{Lithology I\({}_{1-51}\)} & \(\mathbf{l}_{6}\), Sandstones; \(\mathbf{l}_{20}\), Non-vegetated deposit; \(\mathbf{l}_{26}\), Active \\  & non-vegetated scree slope; \(\mathbf{l}_{40}\), Outcropping quartzites; \(\mathbf{l}_{44}\), \\  & Outcropping ypo-abyssal rocks; \(\mathbf{l}_{45}\), Intrusive rocks; \(\mathbf{l}_{46}\), \\  & Outcropping intrusive rocks; \(\mathbf{l}_{49}\), Serpentinites. \\ \hline \multirow{4}{*}{Permeability \(\mathbf{p}_{1-8}\)} & \(\mathbf{p}_{2}\), Cohesive units with low permeability; \(\mathbf{p}_{3}\), Cohesive \\  & units with very low permeability; \(\mathbf{p}_{4}\), Non-cohesive units \\  & with high-medium permeability. \\ \hline \multicolumn{2}{c}{**Categorical ISPs with ERL values\(\geq\)2 or\(\approx\)2**} \\ \hline Land use \(\mathbf{u}_{1-23}\) & \(\mathbf{u}_{2}=\) 2.29, \(\mathbf{u}_{3}=\) 4.48; \\ Lithology I\({}_{1-51}\) & \(\mathbf{l}_{6}=\) 5.19, \(\mathbf{l}_{20}=\) 18.91, \(\mathbf{l}_{26}=\) 5.89, \(\mathbf{l}_{40}=\) 6.15, \(\mathbf{l}_{44}=\) 2.41, \\ Permeability \(\mathbf{p}_{1-8}\) & \(\mathbf{l}_{45}=\) 13.10, \(\mathbf{l}_{46}\mathbf{l}_{46}=\) 19.79, \(\mathbf{l}_{49}=\) 5.52; \\  & \(\mathbf{p}_{2}=\) 1.92, \(\mathbf{p}_{3}=\) 2.06, \(\mathbf{p}_{4}=\) 1.91. \\ \hline \multicolumn{2}{c}{**Continuous field ISPs with ERL values\(\geq\)2**} \\ \hline Aspect (0\({}^{\circ}\)-359\({}^{\circ}\)), **A** & \(\geq\)2: _168–198_, (max **2.07**); \\ Curvature (\(-\)32\(\rightarrow\)29), **C** & \(\geq\)2: _\(-\)24--7_, (max 11.07); +7\(\rightarrow\)17_, (max **5.62**); \\ D. Elevation (350–2906m), **D** & \(\geq\)2: 1737–2104, (max 4.24); 2484–2629, (max **2.31**); \\ Int. Relief (0–111 m, 3 \(\times\) 3 pixels), **I** & \(\geq\)2: _24–56_, (max **5.97**); \\ Slope (0\({}^{\circ}\)–61\({}^{\circ}\)), **S** & \(\geq\)2: 37–57, (max **4.26**) \\ \hline \end{tabular}
\end{table} 
Table 1: Subset is listed of categorical and continuous field ISPs in the Tirano South study area and their respective empirical likelihood ratio values. They will be used for predictions using as DSP the distribution of the set of landslides, **70 at** with **ulpACDIS** as ISPs. Abbreviations for categorical ISPs are \(\mathbf{u}_{1-23}\), land-use classes; \(\mathbf{l}_{1-51}\), lithology units; and \(\mathbf{p}_{1-8}\), permeability classes. For the continuous field ISPs, A, C, D, I, and S are aspect, curvature, digital elevation, internal relief, and slope, respectively. Values are bold if the ELR \(\geq\) 2.00. In Italics is the corresponding range of values, with the maximum ratio in brackets. In this reduced version, only ratios \(\geq\)2 or \(\approx\)2 are shown (table modified after Tables 1 and 2 in [PERSON] et al., 2017 [27]).