Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation Technical Papers, MINING ENGINEERING, Vol. 35, No. 12 December 1983, pp. 1646-1650

M.S. Azun The article unfortunately has some serious flaws negating the usefulness of the paper. The authors claim that kriging (linear kriging) is superior to other methods such as polygon. This is not the case. The deterministic methods (referring to polygon, ID, IDS, etc.) should not be compared with the statistical methods (linear kriging, disjunctive kriging, etc.) because they differ not only in their assumptions, but also their tools used in estimation. Thus, they give different results. By comparing the results of deterministic methods and linear kriging, the authors conclude that polygon, IDS, and linear kriging give an average thickness close to the value obtained from realizations. Besides, they argue that linear kriging gives less variance than the others (Fig. 2). The first conclusion is expected, due to the well-known central limit theorem. The second is the result of the statistical properties of different estimators. Thus, the comparison presented in the paper is rather meaningless because the authors have failed to follow basic statistical procedures. The numerical results of different approaches to an estimation problem cannot be generalized. In conclusion, the paper is not a meaningful contribution, and sadly, quite erroneous. Reply by E.Y. Baafi and Y.C. Kim The two key contentions made by M.S. Azun regarding the paper are: deterministic methods should not be compared with statistical methods and, hence, the results are erroneous; and the paper does not make a meaningful contribution. The first contention is an academic one. Most practitioners in ore reserve estimation could care less whether the tool they are using falls under a deterministic or a probabilistic method, so long as it gives the desired answers. It is probably for this reason that, whenever any new tool such as linear kriging is introduced to practioners in the mining industry, they would like to see a comparison test performed between the existing and the more familiar tools with a new and "strange" tool. Only when a new tool passes such a test, the generally conservative mining community would begin to utilize the new tool to its advantage. The second contention, is a subjective one. The final judgment should be left up to the readers within the mining community. If kriging is accepted more among practitioners, partly due to the paper, then the paper makes a practical contribution to the state-of-the art in ore reserve estimation. Finally, M.S. Azun entirely missed two main points in the paper. The first is that any comparative study of kriging vs. Polygonal or IDS should be performed for local estimation and not for global estimation. In the past, kriging was frequently compared with other existing tools in its performance on global estimation. Such results were nearly identical due to the central limit theorem effect, which further prevented the acceptance of kriging by practitioners. The second point is that a single case study using an existing property, as it was frequently performed in the past, is not sufficient because results depend not only on the tool itself, but also on the nature of the mineralization.