Conditional bias in resource estimation: A simpleguide for practitioners APCOM 2021

Conditional bias occurs when the expected value of the true grade conditional on the estimated grade is not equal to the estimated grade. It is a quantification of how the average of estimates differs from the true value. Conditional bias is present in all resource estimates due to the unavoidable properties of kriging, and indeed all linear estimation (regression) methods. In a mining resource estimation context, the degree of conditional bias is dependent on the spacing of the conditioning data; more data leads to the expectation of less conditional bias This paper discusses conditional bias from two perspectives: 1. 2. Estimates seeking to eliminate, as much as possible, conditional bias; and Estimates that accept a larger amount of conditional bias in resource models, in order to achieve a specific outcome. The problem of conditional bias in estimation can only be fully appreciated if the objective or purpose of a resource model is understood. There are instances where conditional bias should be avoided because it is not reasonable to make decisions using estimates that are known to be wrong in expected value; for example, when making a final decision in grade control with respect to the destination of the material. In most instances in the mining resource estimation context, however, the estimated values will not be “final estimates”, but “interim estimates”, meaning that in the future more data will be obtained, and the ”interim estimate” will then be updated. In this context, the most useful resource model is an interim model that is able to predict the final model estimates, despite not having all the data available that will be collected in the future. This is the objective, for example, of a recoverable “long-term” model developed prior to operating a mine, for example at the feasibility stage. It attempts to predict the ore that a processing plant will receive, well into the future. In such cases, it can be unequivocally demonstrated that conditional bias is not only unavoidable, it is a necessity.