## 2 Materials and Methods
### Research Methods and Ideas
#### 2.3.2 Research Ideas  
To avoid overfitting, excessive redundancy, and pseudo-correlation among influencing factors, and to improve model realism, the Pearson correlation coefficient was applied to test and screen the influencing factors. When the correlation coefficient of two influence factors is greater than or equal to 0.8, it indicates a strong correlation between the two influence factors. For factors showing strong correlation, their contribution rates in the MaxEnt model pre-simulation were compared, retaining the factor with the higher contribution to grassland fire. Based on both the correlation and contribution rate, the selected factors for natural grassland fire model training included distance to river, relative humidity, mean annual wind speed, mean annual precipitation, slope, slope aspect, and vegetation type. The factors selected for anthropogenic grassland fire model training included NDVI, relative humidity, population density, distance to settlements, distance to roads, slope, slope aspect, mean annual temperature, the human footprint index, and distance to rivers. In the modeling process, 75% of the fire point samples were randomly selected as the training set, while the remaining 25% served as the test set for model prediction. To minimize errors, the MaxEnt model was run 10 times, and the results were averaged to generate the ROC curve, the spatial distribution map of grassland fire susceptibility, and the response curves of the influencing factors. Additionally, the model's maximum training sensitivity and specificity (WTSS), balanced training omission rate, and predicted area-level threshold (TPT) were employed as categorization thresholds for identifying high-susceptibility and low-susceptibility zones. The reliability and accuracy of the grassland fire susceptibility evaluation results were evaluated using the receiver operating characteristic (ROC) curve. The area under the ROC curve (AUC) serves as a key metric for evaluating the model's performance, with AUC values ranging from 0 to 1; a value closer to 1 signifies greater prediction accuracy. The evaluation criteria are typically defined as follows: [0, 0.6) indicates prediction failure; [0.6, 0.7) is considered poor; [0.7, 0.8) is average; [0.8, 0.9) is good; and [0.9, 1] is classified as excellent. The AUC value for the natural grassland fire susceptibility prediction model was 0.947 (\(\pm\)0.024), while the AUC for anthropogenic grassland fires was 0.978 (\(\pm\)0.002) (Figure 2). These results demonstrate that the accuracy and reliability of the model's predictions in both scenarios are at an excellent level, confirming a high accuracy in simulating grassland fire susceptibility distribution areas. Assessing accuracy exclusively through the AUC presents several limitations [45]. Kvamme gain statistics mainly reflect the overall accuracy of the model but do not account  
Figure 2: ROC curve for grassland fires. for the accuracy of geospatial partitioning, and they may, at times, fail to accurately represent the actual conditions. For example, an overly broad delineation of high-susceptibility areas may increase government funding and management costs. Consequently, Kvamme gain statistics are a valuable tool for validating the accuracy of site prediction models [46,47]. \[G=1-\frac{P_{a}}{P_{s}} \tag{1}\]  
where \(G\) represents the gain statistic value; \(P_{a}\) denotes the proportion of the predicted area to the total study area; and \(P_{s}\) denotes the proportion of prairie fire sites within the predicted area to the total number of fire sites in the study area. If \(G>0\), it indicates that the model is effective in predicting prairie fires, with values closer to 1 signifying better prediction accuracy. When \(G=0\), it suggests that the model has limited or no predictive capability for prairie fires, whereas when \(G<0\), the model demonstrates inverse predictive ability, predicting the likelihood of non-existence of grassland fires.