Uncertainty Assessment for IDW Ore Grade Estimates

As a typical ore grade estimation method, inverse distance weighting (IDW) has a long-time standing deficiency in reliability evaluation for its estimates, which has seriously limited its practicability. A statistical solution is presented in this paper to address the issue. A key character of IDW, that weight of each participation sample is the probability that the current un-sampled value is equal to the corresponding sample value, is proposed and proved by considering the participation samples as cutoff values during an indicating process. Based on this character, the conditional cumulative distribution function (CCDF) models related to the points to be estimated are constructed to fully characterize the uncertainty of IDW estimates. At last, a case study is carried out using cross validation and a test dataset from exploration engineering of a real ore-body. It is found that the real character of test dataset has been successfully revealed by the medium, expected and variance drawing from the constructed CCDFs, showing that the theoretical analysis and practical application can prove the validity and practicability of the proposed method to some extent.