Conditional Bias in Kriging: Let’s Keep It

Abstract

Mineral resource estimation has long been plagued with the inherent challenge of conditional bias. Estimation requires the specification of a number of parameters such as block model block size, minimum and maximum number of data used to estimate a block, and search ellipsoid radii. The choice of estimation parameters is not an objective procedure that can be followed from one deposit to the next. Several measures have been proposed to assist in the choice of kriging estimation parameters to lower the conditional bias. These include the slope of regression and kriging efficiency.

The objective of this paper is to demonstrate that both slope of regression and kriging efficiency should be viewed with caution. Lowering conditional bias may be an improper approach to estimating metal grades, especially in deposits for which high cutoff grades are required for mining. A review of slope of regression and kriging efficiency as tools for optimization of estimation parameters is presented and followed by a case study of these metrics applied to an epithermal gold deposit. The case study compares block estimated grades with uncertainty distributions of global tonnes and grade at specified cutoffs. The estimated grades are designed for different block sizes, different data sets, and different estimation parameters, i.e., those geared toward lowering the conditional bias and those designed for higher block grade variability with high conditional biases.