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Journal of the Southern African Institute of Mining and Metallurgy

On-line version ISSN 2411-9717

Abstract

CLARK, I.. Regression revisited (again). J. S. Afr. Inst. Min. Metall. [online]. 2015, vol.115, n.1, pp. 45-50. ISSN 2411-9717.

One of the seminal pioneering papers in reserve evaluation was published by Danie Krige in 1951. In that paper he introduced the concept of regression techniques in providing better estimates for stope grades and correcting for what later became known as the 'conditional bias'. In South Africa, the development of this approach led to the phenomenon being dubbed the 'regression effect', and regression techniques ultimately formed the basis of simple kriging in Krige's later papers. In the late 1950s and early 1960s, Georges Matheron (1965) formulated the general theory of 'regionalized variables' and included copious discussion on what he termed the 'volume-variance' effect. Matheron defined mathematically the reason for, and quantification of, the difference in variability between estimated values and the actual unknown values. In 1983, this author published a paper that combined these two philosophies so that the 'regression effect' could be quantified before actual mining block values were available. In 1996 and in some earlier presentations, Krige revisited the regression effect in terms of the conditional bias and suggested two measures that might enable a practitioner of geostatistics to assess the 'efficiency' of the kriging estimator in any particular case. In this article, we revisit the trail from 'regression effect' to 'kriging efficiency' in conceptual terms and endeavour to explain exactly what is measured by these parameters and how to use (or abuse) them in practical cases.

Keywords : geostatistics; block estimation; regression effect; conditional bias; kriging efficiency.

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