Minimum variance or maximum profitability?

CIM Bulletin, Vol. 80, No. 901, 1987

R. MOHAN SRIVASTAVA, Department of Applied Earth Sciences, Stanford University, Stanford, California

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.

Keywords: Estimation, Mining industry, Ore classification, Geostatistics, Applied geology.