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Kriging variance

 

The kriging variance rises up to a maximum and then drops off.
This behavior has been described by Brooker (1986).

These remarks about the bizarre behavior of the kriging variance crop up in "A study on kriging small blocks", a paper coauthored by Margaret Armstrong and Normand Champigny and published in CIM Bulletin, March 1989, under the category Ore Reserve Estimation. Apparently troubled by the rise and fall of the kriging variance, the authors refer to Brooker for an explanation but, inexplicably, Brooker praises its robustness! The ugly fact of the matter is that geostatistical scholars supplanted the variance of a central value with the pseudo "kriging variance" of a set of central values.

That sort of paper invariably passes with flying colors the scrutiny of CIM Bulletin's reviewers such as Dr A J Sinclair, PEng, PGeo, and Mr M Vallée, PEng, My encounters with geostatistical peer reviewers taught me that they protect their turf with brazen disregard for scientific integrity and professional ethics. In fact, David, the author of Geostatistical Ore Reserve Estimation, and Sinclair reviewed and rejected Precision Estimates for Ore Reserves before similarly challenged scholars such as Armstrong, Dowd, Froideveaux, Journel, and several anonymous reviewers, dismissed the fundamentals of probability theory and mathematical statistics.

Here are the scientific facts in a nutshell! In mathematical statistics, each distance-weighted average has its own variance, and the variance of a set of distance-weighted averages is a meaningless measure for variability and precision. In geostatistics, however, each set of kriged estimates has its own pseudo "kriging variance" that can be used to oversmooth, smooth to perfection, and perhaps even to undersmooth. I offered $1,000 to the first geostatistician who showed how to calculate unbiased confidence limits for contents and grades of ore reserves without taking degrees of freedom into account. Not a single response was received! Meanwhile, I obtained 95% confidence intervals and ranges for the gold content and grade of a reserve on the basis of test results for more than 300 boreholes with spreadsheet software only. Borehole statistics with spreadsheet software, a paper that explains show how to fingerprint boreholes and how to calculate confidence limits in six stages, is posted under Reviewed papers.

In 1989, twelve years after David's textbook was published Armstrong and Champigny still didn't know why kriging variances rise and fall. Nonetheless, they went into kriging crisis management by issuing a decree against oversmoothing. In other words, the requirement of functional independence can be violated a little but not a lot. CIM Bulletin, unfailingly at the leading edge of geostatistics, has already reviewed and published a paper on perfect smoothing.

 

 
 
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