Minimum variance or maximum profitability?

"The goal of estimation is considered in the light of decision analysis. A simple example reveals the essential elements of decision-making in the face of uncertainty. A second example shows that these elements are also key features of many mining decisions. These two examples cause us to revive an old probabilistic notion that the goal of estimation should be to quantify what is unknown. The conditional probability distribution provides the complete statement of one's uncertainty. Once the conditional probability distribution has been established, one should retain as an estimate the value which minimizes some objective loss function. A third example shows how the ""best"" estimate depends on the chosen loss function. Current practice is almost exclusively based on the least squares method, which assumes a loss function which penalizes underestimation and overestimation equally. This is unfortunate not only because symmetry is an unrealistic assumption but also because mining offers a rare opportunity to state the loss function directly in terms of profitability. Both the theoretical framework and the practical tools exist to allow us to reconsider the conventional notion of the ""best"" estimate. IntroductionThis paper looks at estimation in the mining industry from the point-of-view of decision analysis. Virtually all decisions depend on estimates since few of the important parameters are ever known exactly. In this paper we will be referring mainly to the estimation of ore grades, though the approach discussed here is generally applicable to any decision in which relevant information is uncertain.In the first section we look at a very simple example of decision-making in the face of uncertainty. We will then tum to a mining example and see that the essential features of the simple example still pertain. From these two examples it will be clear that the decision analysis approach rests on two key concepts: the conditional probability distribution and the loss function. A third example demonstrates how different loss functions produce different ""best"" estimates from the same conditional probability distribution. In the final sections we willexamine the current practice of estimation in the mining industry. Though the tools for estimating the conditional probability distribution already exist, a change in the way we think about ""best"" estimates is needed. Very little attention is presently paid to the loss function even though it is readily available in many mining applications."