Evaluating the Uncertainty and Predictive Performance of Probabilistic Models Devised for Grade Estimation in a Porphyry Copper Deposit

Abstract

Probabilistic models are used to describe random processes and quantify prediction uncertainties in a principled way. Examples include geotechnical and geological investigations that seek to model subsurface hydrostratigraphic properties or mineral deposits. In mining geology, model validation efforts have generally lagged behind the development and deployment of computational models. One problem is the lack of industry guidelines for evaluating the uncertainty and predictive performance of probabilistic ore grade models. This paper aims to bridge this gap by developing a holistic approach that is autonomous, scalable and transferable across domains. The proposed model assessment targets three objectives. First, we aim to ensure that the predictions are reasonably calibrated with probabilities. Second, statistics are viewed as images to help facilitate large-scale simultaneous comparisons for multiple models across space and time, spanning multiple regions and inference periods. Third, variogram ratios are used to objectively measure the spatial fidelity of models. In this study, we examine models created by ordinary kriging and the Gaussian process in conjunction with sequential or random field simulations. The assessments are underpinned by statistics that evaluate the model’s predictive distributions relative to the ground truth. These statistics are standardised, interpretable and amenable to significance testing. The proposed methods are demonstrated using extensive data from a real copper mine in a grade estimation task and are accompanied by an open-source implementation. The experiments are designed to emphasise data diversity and convey insights, such as the increased difficulty of future-bench prediction (extrapolation) relative to in situ regression (interpolation). This work enables competing models to be evaluated consistently and the robustness and validity of probabilistic predictions to be tested, and it makes cross-study comparison possible irrespective of site conditions.