## 4 Results and Discussion
### Construction of a Quantitative Optimization Model for Prospecting Target Areas
Then, 4943 ore-free units without minerals and 109 known ore-bearing units were randomly selected. Using a stepwise discriminant model in SPSS software, we constructed the \"Quantitative Optimization Model for Regional Prospecting Targets for Au Mineralization in the Beishan Area of Gansu Province II\". The parameters of the model are shown in Table 2.  
\[\text{R2}=\text{SiO}_{2}\times 0.216-\text{Au}\times 0.119+\text{Zr}\times 0.012+ \text{CaO}\times 0.064+\text{Sr}\times 0.002+\text{MgO}\times 0.153+\text{Mn} \times 0.001-\text{$\Delta$Td}\times 0.002-20.08 \tag{4}\]  
The results of model II's optimization are as follows: The discriminant function (model II) presented in Table 2 is employed to calculate the discriminant value (R2) of each research unit within the \"Au mineralization exploration information modeling database\" (24,824 \(\times\) 42), which encompasses the Beishan area. The discriminant threshold value is R0, which is \(-\)0.89. Units with an R2 value less than this are deemed to be ore-bearing units. Model II identifies 665 research units as preferred ore-bearing units, of which 78 are known ore-bearing units, representing 11.73% of the total number of preferred ore-bearing units. This figure is 26.66 times higher than the proportion of units with minerals (0.44%). 3. Model III  
Following the removal of the ore-bearing units of preference identified by models I and II, 4943 ore-free units and 109 known ore-bearing units were randomly selected and processed using the stepwise discriminant model in SPSS software. This formed the basis of the \"Quantitative Optimization Model for Prospecting Target Areas for Au Mineralization Information in the Beishan Area of Gansu Province III\". The model parameters are presented in Table 2.  
\[\text{R3}=-\text{Auh}\times 1.821-\text{Y}\times 0.126+\text{Al}_{2}\text{O}_{ 3}\times 0.341+\text{$\Delta$Tx}\times 0.002+\text{V}\times 0.026+\text{B} \times 0.022+\text{CaO}\times 0.105-\text{Pb}\times 0.029 \tag{5}\]  
The results of model III's optimization are as follows: The discriminant function (model III) in Table 2 is used to calculate the discriminant value (R3) of each research unit in the \"Au mineral exploration information specification unit modeling database (24,824 \(\times\) 42)\" in the Beishan area. R0 = \(-\)1. 41 is the critical value of the discriminant, and R3 \(<\) R0 determines that the research unit is a preferred ore-bearing unit, and model III identified 550 research units as preferred ore-bearing units, of which 21 are known ore-bearing units, accounting for 3.81% of the total number of preferred ore-bearing units, which is 8.68% higher than the proportion of units with minerals (0.44%). 4.2. Discussion of the Model's Validity  
1. The effectiveness of optimal model I: Mathematical validity analysis:The F-test is represented by the following equation [62; 63; 64]:  
\[\text{Fp}= \frac{NA+NB-P-1}{(NA+NB-2)P}\times\frac{NA\times NB}{NA+NB}D2 \tag{6}\]  
where F\({}_{\text{P}}\) is the F-distribution value calculated by the discriminant function (model); F\({}_{0.01}\) is the theoretical value of the F-distribution table (obtained by checking the F-test table) at the significance level of 0.01 (1% error); A and B are the two discriminant classification populations (A--discriminant ore-bearing unit population; B--discriminant non-ore-bearing unit population); NA and NB are the sample sizes of the two populations, respectively; D2 = \(\overline{\text{R}}\)A - \(\overline{\text{R}}\)B (Marth distance); and P is the first degree of freedom (number of variables). When F\({}_{\text{P}}\) > F\({}_{0.01}\), the two total samples are significantly different, and the constructed discriminant function (model) is effective in discriminating between unknown samples. In Table 2, F\({}_{\text{P}}\) = 16.26, which is much larger than F\({}_{0.01}\) = 3, indicating that the constructed discriminant model is highly effective. Preferred model I in Table 2 has a positive prediction rate of 82.2% for ore-bearing units and 98.3% for non-ore-bearing units.