Figure 2: Top: the omnidirectional semi-variogram of the first and second principal components. Bottom: the blue dots constitute the irregular grid on which GPR will be performed, while the red dots are the data. 4. Key Results, Outcomes, or Insights Once an irregular grid is defined, GPR simulation of the principal components PC1 and PC2 can be performed independently. Figure 3 shows GPR simulated realizations of PC1 and PC2 projected onto the X1–X2 space with the original observations overlaid for reference. Figure 3: Example of GPR simulated realizations of PC1 and PC2 projected onto the 1– 2 space. Figure 4 (left) shows GPR interpolation in PC space (PC1 vs. PC2, blue) overlaid with the observed PC scores (red). We can back-transform the model interpolation (posterior) to the actual Y space ( 1 vs. 2) where we can see that by honoring the data, the model yields variability-consistent estimates ( ̂1 and ̂2) in the gaps, as shown in Figure 4 (right). Now, one can identify the efficient frontier for 1 and 2 to optimize the phosphate flotation process (Figure 5, top). Each point along this frontier represents a Pareto-optimal trade-off, which can be mapped back to the predictor
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