Reliability of NIR Chemometric Models: Methodology to Determine How Many Samples Are Required to Calibrate a Model for Accurate Prediction

Near-infrared spectroscopy (NIR) is an emerging powerful tool with widespread applications across various industries, including mineral exploration and geo-metallurgical characterization. This technique is particularly attractive from an operational standpoint due to its ability to perform rapid and non-destructive measurements. In the geometallurgical field, NIR is primarily employed for the identification of NIR-active minerals that collectively influence the production process. A predictive mathematical model used to estimate a numeric value, like hardness, from a NIR spectral curve, may be referred to as a "chemometric model", represented by a function. The accuracy of chemometric models, like all predictive models, is highly reliant upon the availability of enough calibration samples to mathematically establish a relationship between the target variable and spectral signatures. The objective of this study is to present a methodology to evaluate the amount of calibration samples required to produce a sufficiently accurate chemometric model. An inverse function developed to simulate different scenarios of spectral curves is used. This tool enables the generation of multiple chemometric functions by varying the amount of data used for calibration. By employing an inverse function, it is possible to analyze how the number of calibration samples influences the associated variability or error. This approach allows for the establishment of a quantitative relationship between the calibration dataset size and the predictive model's reliability by calculating the percentage error from iterations using the simulated values. This study aims to determine the minimum number of samples required for the calibration of the chemometric model to ensure a prediction error below 3% for a specific target variable, demonstrated using hardness prediction. It is crucial that the selected calibration samples are spatially representative and free from sampling biases. It is important to highlight that the total error in the block model (for subsequent use in mine planning) results from the propagation of multiple sources of uncertainty, including QAQC, chemometric model reliability, NIR sample representativity, and the interpolation methodology used in the block model. However, this analysis focuses exclusively on the variability associated with the reliability of the chemometric model. This methodology was tested in a simulated case study and in a porphyry copper deposit in northern Chile.