## 4 Uncertainty Analysis
### Model Selection and Application
#### 4.2.2 Coupled Model  
A coupled model combines two or more models, integrating the strengths of each model to effectively enhance the predictive accuracy of the overall model [108]. [PERSON] et al. [109] combined the deterministic coefficient method with the SVM model, while [PERSON] et al. [110] integrated the deterministic coefficient method with the logistic regression model. Both studies confirmed that the evaluation results of the coupled model were more accurate than those of single models. In previous examples in the literature, coupled models are mainly classified into two categories: coupling between data statistical models and machine learning models, and coupling between machine-learning models. The coupling of data-driven models with machine-learning models is illustrated in Figure 4. The main principle involves using the data-driven model (Model 1) to calculate the influence values of various evaluation factors, which are then used as inputs for the machine learning model (Model 2), ultimately yielding the prediction results. [PERSON] et al. [108] utilized 1081 historical landslide data points from the Wenchuan region, along with 13 evaluation factors including terrain, geological structure, meteorology, hydrology, etc. They established three individual models of LR, SVM, and RF, as well as three coupled models integrating the certainty factor (CF). Comparative analysis of the predictive results from these six models revealed that the CF-RF model exhibited the highest prediction accuracy. Furthermore, the predictive accuracy of the coupled models surpassed that of the corresponding individual models, suggesting that coupling models can enhance the predictive accuracy of individual models to a certain extent. [PERSON] et al. [111] and [PERSON] et al. [112] both employed a combination of geographic detectors and machine learning models. By optimizing the evaluation factors, they improved the accuracy of the assessment results. This demonstrates that coupled models have certain advantages over individual models. [PERSON] et al. [79] conducted a landslide susceptibility assessment in Xining City using GF-2 remote sensing imagery data and field survey results to delineate landslide locations. They selected factors including slope, aspect, curvature, the topographic wetness index (TWI), relative slope position (RSP), lithology, distance to faults, distance to rivers, and distance to roads, based on the actual conditions of the study area, to construct a landslide susceptibility evaluation index system. Subsequently, they employed three coupled models: frequency ratio-random forest (FR-RF), frequency ratio-support vector machine (FR-SVM), and frequency ratio-artificial neural network (FR-ANN) for landslide susceptibility assessment in the study area. The results (Figure 5) indicated that the distribution of landslide susceptibility levels among the three models was largely consistent, with high susceptibility areas mainly being concentrated in the northeast part of the study area, and with over 87% of landslides occurring in moderate to high-susceptibility zones. This suggests that the predictive results of the three machine learning models are generally consistent with the actual situation. The AUC values of the three models were: 0.863 (FR-RF), 0.839 (FR-ANN), and 0.825 (FR-SVM), all exceeding 0.8, indicating good predictive accuracy for all models. Among them, the FR-RF model had the highest AUC value, indicating better predictive capability, making it more suitable for landslide susceptibility assessment in regions with similar geographic environments. Figure 4: Data-driven model and machine learning model coupling diagram. Research has shown [113] that using statistical models as input variables for machine learning models can assign the numerical expression of landslide susceptibility as the quantified weight values for evaluation indicator sub-intervals. This approach helps to standardize all variables to similar scales, thereby simplifying the machine learning model.