<p>Conventional evaluation of mineral resource interpolation emphasizes predictive accuracy and reporting compliance, but these criteria do not directly characterize the stability of estimation outputs with respect to method choice. This study introduces an Mutual Information and Entropy Based Interpolation Uncertainty Indicator (MUI) as a diagnostic measure of method-conditioned instability. MUI is defined from normalized entropy and normalized mutual information over controlled realization ensembles, and evaluates the coherence and stability of interpolation outputs under a prescribed realization protocol. In the case study, comparable multi-realization ensembles were constructed for inverse distance weighting (IDW) and ordinary kriging (OK) for Cu estimation in the skarn and hornfels domains of a heterogeneous porphyry-skarn deposit. The results show that OK produced a less coherent and less stable realization ensemble than IDW, with the contrast most evident in skarn. At the same time, conventional benchmarking against infill drilling data indicates that both methods remained comparatively accurate in both skarn and hornfels. These results show that realization stability and interpolation accuracy describe different aspects of estimation behavior. MUI therefore provides a useful complement to conventional validation by capturing method-dependent differences that standard accuracy-based frameworks do not directly express. Although MUI does not explicitly quantify total methodological uncertainty, it can serve as a practical diagnostic of potential method-induced bias. Interpreted together with infill-drilling benchmarking and constrained resampling, the results further provide a safety-oriented assessment of interpolation behavior in terms of accuracy, robustness, and explainability.</p>

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Diagnosing method conditioned bias in mineral resource estimation using a mutual information and entropy uncertainty indicator

  • Xiaoqing He,
  • Yuhan Huang,
  • Bin Wu,
  • Yingchun Ao,
  • Haijun Jiao

摘要

Conventional evaluation of mineral resource interpolation emphasizes predictive accuracy and reporting compliance, but these criteria do not directly characterize the stability of estimation outputs with respect to method choice. This study introduces an Mutual Information and Entropy Based Interpolation Uncertainty Indicator (MUI) as a diagnostic measure of method-conditioned instability. MUI is defined from normalized entropy and normalized mutual information over controlled realization ensembles, and evaluates the coherence and stability of interpolation outputs under a prescribed realization protocol. In the case study, comparable multi-realization ensembles were constructed for inverse distance weighting (IDW) and ordinary kriging (OK) for Cu estimation in the skarn and hornfels domains of a heterogeneous porphyry-skarn deposit. The results show that OK produced a less coherent and less stable realization ensemble than IDW, with the contrast most evident in skarn. At the same time, conventional benchmarking against infill drilling data indicates that both methods remained comparatively accurate in both skarn and hornfels. These results show that realization stability and interpolation accuracy describe different aspects of estimation behavior. MUI therefore provides a useful complement to conventional validation by capturing method-dependent differences that standard accuracy-based frameworks do not directly express. Although MUI does not explicitly quantify total methodological uncertainty, it can serve as a practical diagnostic of potential method-induced bias. Interpreted together with infill-drilling benchmarking and constrained resampling, the results further provide a safety-oriented assessment of interpolation behavior in terms of accuracy, robustness, and explainability.