# Optimized Weighted Ensemble Approach for Enhancing Gold Mineralization Prediction
## 2 Method
### Predication Approaches
#### 2.1.1 Geostatistical Technique  
Ordinary Kriging  
Geostatistics is a better prediction method than traditional methods. Kriging algorithms are widely regarded as the best linear unbiased estimator capable of producing reliable estimates even for locations that have not been sampled [29]. A linear combination of a number of nearby values is used to determine the overall result, with weights given to minimize the variation in the predicted value. Lagrangian multipliers are a valuable tool for determining the weights that should be used when normalization is a consideration. Kriging uses the variogram model to quantify the autocorrelation pattern in the research region [30]. The variogram is produced by taking the average of the semi-variances, which are computed as follows for each combination of locations and distance bin, and then plotting the results:  
\[\gamma(h)=\frac{1}{2}E[\{Z(x)-Z(x+h)\ ^{2}\}] \tag{1}\]According to this formula, the semi-variance between any two locations separated by the vector h is denoted by \(\gamma(h)\) (the lag distance). The semi-variance is half of the anticipated square difference between two values of the variable Z, specifically Z (x) and Z (x + h), which are differentiated by the vector h. This is how the semi-variance is defined. An essential part of kriging is the sampling strategy used. This method needs samples to be divided by various lag lengths, from minor to very large, to ensure that the variogram can accurately portray the spatial complexity of the area. This is crucial for obtaining a dependable variogram model and enabling kriging to achieve its optimum precision. On the other hand, kriging assumes a linear relationship between samples. Additionally, the structural data required for the Kriging method (i.e., the covariance or variogram) is based on two-point statistics. As a result, kriging may not always be sufficient to represent the comprehensive nature of spatial nonlinearity and complex features. Second-order stationarity is when the mean and standard deviation are both the same across the study area, and the covariance depends only on the lag distance h (where h is a vector that includes the size of the distance between the data pairs and the direction of the line that connects them) [31; 32]. The formula for the OK estimator is as follows:  
\[Z*(x_{0})=\sum_{i=1}^{m}\mathrm{a}\mathrm{i}Z(x_{i}) \tag{2}\]  
Since extremely positive values significantly affect semi-variance calculations, kriging is extremely sensitive to skewed distributions. This makes it possible for Kriging estimations to be unreliable [30]. According to [PERSON] (1983) [33], indicator kriging is a nonparametric approach for evaluating the likelihood of multiple threshold values, \(Z_{k}\), given geographical data. The first thing that must be performed in order to use the kriging indicator (IK) is to convert it into indicators [34]. This is accomplished by giving the values 0 and 1 in the binary system to grades that are, respectively, above and below a particular cut-off. The explanation is the binomial coding of the data as either 1 or 0, depending on how it is connected to the specified \(Z_{k}\) cut-off number [35]. For any given value, \(Z(x)\):  
\[i(x,Z_{k})= \begin{cases}1,ifZ(x)\leq Z_{k},\\ 0,ifZ(x)>Z_{k}\end{cases}  \tag{3}\]  
The indicator variogram is combined with a weighted average of the indicator values at the sample sites to estimate the IK at the unsampled point. A variogram of indicators is the distribution of the variance of the indicator function at varying distances and orientations from a sample point (1 if the variable is present and 0 otherwise). Indicator kriging has several advantages, including the ability to use complex data and soft data and the ability to estimate the probabilities of occurrence for a binary or categorical variable. However, it requires many samples to provide reliable estimates and can be affected by outliers. It also requires software proficiency and a strong understanding of spatial statistics and geostatistics [36].