Statistical Methods For Mineral Engineers ⭐ Complete
Modern practice uses weighted least squares, where each measurement is assigned a variance (from sampling and analytical error). Measurements with low variance receive small adjustments; bad actors receive large adjustments—flagging them for review.
Practical output: A reconciled feed grade that is statistically more reliable than any single direct measurement.
Classical (frequentist) statistics asks: "What is the probability of the data given a null hypothesis?" Bayesian statistics asks: "What is the probability of the hypothesis given the data?"
For mineral engineers, this is revolutionary.
Application: Grade Control Prior to drilling, you have a prior belief (based on geological model) that the block grade is ~0.5% Cu. You drill a blasthole and get an assay of 1.0% Cu. Bayesian updating combines the prior (0.5% ± 0.2 variance) with the new evidence (1.0% ± 0.1 lab variance) to produce a posterior estimate. Result: If the prior is very strong (low variance), the final estimate might be 0.6% Cu, not 1.0%. You "shrink" the extreme estimate towards the mean, reducing over-reaction to single assays. Statistical Methods For Mineral Engineers
The cornerstone of mineral resource estimation is the variogram. The variogram quantifies spatial continuity.
$$ \gamma(h) = \frac12N(h) \sum_i=1^N(h) [Z(x_i) - Z(x_i + h)]^2 $$
Where $\gamma(h)$ is the semivariance, $h$ is the lag distance, and $Z$ is the grade.
Mineral engineers must identify three key features of the variogram: Modern practice uses weighted least squares, where each
How do you know if your lab results are accurate? Statistics are the backbone of Quality Assurance/Quality Control (QAQC).
Monday 8:00 AM – You see this:
| Hour | Head Grade (% Cu) | Tails Grade (% Cu) | |------|------------------|--------------------| | 6 AM | 0.95 | 0.08 | | 7 AM | 0.88 | 0.09 | | 8 AM | 0.97 | 0.14 |
Statistical check:
Calculate moving range of tails: 0.01 → 0.05.
Upper control limit (UCL) = 0.08 + 3σ ≈ 0.13.
8 AM tails = 0.14 → Out of control. The cornerstone of mineral resource estimation is the
Action: Immediately check collector addition and froth depth. Don’t wait for more samples.
| Pitfall | Consequence | Statistical Remedy | | :--- | :--- | :--- | | Using mean instead of median | Overestimates plant feed grade | Report P50, P90, and mean. Use geometric mean for lognormal data. | | Ignoring nugget effect in variograms | Underestimates short-scale variability | Perform rigorous variography with lag spacing < 10m. | | Applying t-tests to autocorrelated data | Massive type I error (false positives) | Use time-series control charts or pre-whiten data. | | Overfitting with stepwise regression | Model fails on new data | Use cross-validation or regularization (LASSO, ridge). | | Pseudoreplication in flotation tests | Inflated degrees of freedom | A single cell with 5 assays is not 5 replicates. Average first, then test across true replicates. |
Report ID: SME-STAT-2025-04
Target Audience: Plant Metallurgists, Mine Geologists, Process Engineers
Core Message: In a world of inherently variable ore, statistics is not just about averages—it’s the science of making confident decisions despite chaos.
Today’s mineral engineer has access to automated mineralogy (QEMSCAN, MLA), NIR sensors, and laser diffraction. This creates high-dimensional data.