Confidence limits for mineral reserves and mineral resources

What keeps the world’s mining industry going is mineral exploration. To find and define mineral reserves and mineral resources is not just the name of the game but is itself a bit of a game. The trouble is statistically challenged qualified persons infer ore between holes before verifying spatial dependence either within holes or between holes. To infer ore between holes worked miracles when Bre-X drilled holes at a spacing of 50 m up to 200 m. When this geostatistical practice was applied at Bre-X’s Busang property, it didn’t spook the Ontario Securities Commission (OSC) until a few barren holes were twinned. But it really fooled Bre-X’s stakeholders, didn’t it?

Bre-X’s inferred phantom gold resource passed David’s famous pudding test with a parade of red flags flying. Yet, it was an cinch to prove nothing but barren rock between salted holes. Bre-X’s boss salter didn’t even know how to create spatial dependence between ordered sets of bogus gold grades. Not that it would have mattered. In 2008 qualified persons still do not know how to verify spatial dependence by applying analysis of variance to the variance of a set and the first variance term of the ordered set. But did they ever know how to infer phantom gold between Busang’s barren holes. The trouble with qualified persons is they don’t want to test for spatial dependence between measured values in ordered sets.

There’s more to the Bre-X salting scam than swindled shareholders were told. The 1998 Interim Report on Setting New Standards doesn’t make an easy read. I was pleased because the Mining Standards Task Force (MSTF) talked about real statistics in ore reserve estimation where surreal geostatistics had ruled supreme since the 1990s. But MSTF’s best-laid plan for real statistics in ore reserve estimation came to naught because the odd geostat guru turned bold again and bounced back after the Bre-X fraud. What replaced the Mining Standards Task Force and its 1998 Interim Report was CIM Standing Committee of Reserve Definitions and its National Instrument 43-101 Standards of Disclosure for Mineral Projects. CIM’s definitions were all about weasel words and window dressing with loads of twists and turns. Some sort of show but don’t tell. It sported as many sound sampling practices and proven statistical methods as the Philosopher’s Stone. And much of it was crafted by the most jaded geostatistical mind West of the Rocky Mountains.

To assume the continuity of mineralization between ordered sets of measured values was all the rage among geostatistically gifted ore reserve practitioners in the early 1990s! I myself like to infer because I grew up with sampling and statistics. To infer has the ring of true statistics in my little world. I know statistical inferences and degrees of freedom belong together like donuts and holes. And I even know why! To assume, krige, smooth and rig the rules of statistics was never an option in my work! What I did do is derive confidence limits for the weighted average grade of each hole. Matheron didn’t derive the variance of the length-weighted average for a set of core samples with variable lengths in 1954. So I derived it in 1994. I always verify spatial dependence between measured values in ordered sets. It doesn’t matter whether core samples vary in length, in density, or in both length and density. Statistics gives confidence limits for metal grades and contents as an intuitive measure for risk. And it gives confidence limits that take into account a significant degree of spatial dependence between measured values in ordered sets. This is why it’s so much fun to work with real statistics but kind of silly to put up with surreal geostatistics.

Mines do not like confidence limits for mineral reserves in annual reports because it’s a promise of sorts to mining investors. When mines ship mineral concentrates or mined ores to other mines or to smelters, they like confidence limits for metal contents and grades as a measure for risk. So what gives? I told John Drury, Chair, CIM Ad Hoc Reserve Definitions Committee and OSC’s mining expert, that ISO Technical Committee 183 derived unbiased confidence limits for metal contents and grades of mineral concentrates and mined ores. Drury didn’t grasp why the very same method does give 95% confidence intervals and ranges for metal contents and grades of mineral reserves. I liked John Drury because he made time to listen to my story. The year was 1994 and Bre-X’s was busy at Busang!

Geostatistically engineered mineral reserves may bode well in annual reports but are bound to shrink when mined. Geostatisticians do not know how to derive unbiased confidence limits for metal contents and grades. Pollsters do report confidence limits for opinion surveys because they work with real variances. Geostatisticians work with pseudo kriging variances and do not get unbiased confidence limits. So what’s the matter with the average geostatistical mind? The quintessence is that Agterberg fumbled the variance of the distance-weighted average first in 1970 and again in 1974. It’s a tale of two fumbles so to speak. What baffles me is that not a single geostatistician has asked Agterberg to explain why his distance-weighted average point grade does not have a variance. When will the world’s mining industry ask that question? When will it be ready to replace Matheron’s statistical madness with sound sampling practices and proven statistical methods?

Leave a Reply

Your email address will not be published. Required fields are marked *