In the world of mineral engineering, decisions have billion-dollar consequences. A mill that operates at 85% recovery instead of 90% can render a deposit uneconomical. A misinterpreted assay grid can lead to the development of a barren hill. Unlike chemical engineering (which deals with pure reactants) or mechanical engineering (which deals with deterministic tolerances), mineral engineering must contend with heterogeneity .
If $X$ is the vector of measured variables and $V$ is the variance-covariance matrix of measurements, we find the adjusted values $\hat{X}$ that minimize:
Low-precision measurements (e.g., a problematic conveyor scale) get adjusted more than high-precision measurements (e.g., a calibrated lab balance). The output is a single, coherent set of production data. Part 6: Regression Analysis for Recovery Optimization Linear regression is the workhorse, but mineral processes are rarely linear. Logistic Regression Recovery is a proportion between 0 and 1. Linear regression can predict values outside this range ($>100%$). Logistic regression models the log-odds of recovery: Statistical Methods For Mineral Engineers
Statistically, we have redundant data. You have 3 assays (Feed, Con, Tail) and 2 flow rates (Feed, Tail). The system is over-determined . Modern metallurgical accounting uses minimization of weighted sum of squares to adjust measurements so they obey the conservation of mass (tonnage and metal).
Modern mineral engineering is no longer about "the best guess of the chief metallurgist." It is about probabilistic forecasting , quantified risk , and data-driven optimization . Engineers who ignore statistics are not practicing engineering; they are gambling. Those who master the variogram, Gy’s formula, and Bayesian updating will be the ones who unlock value from complex orebodies in a volatile commodity market. In the world of mineral engineering, decisions have
$$ \ln\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 X_1 + ... + \beta_n X_n $$
A copper porphyry deposit. Inverse distance weighting might over-weight a single high-grade assay near a fault. Kriging detects the anisotropy (directionality) and assigns weights based on the continuity along the ore body vs. across it. Part 3: Sampling Theory – Gy’s Formula Pierre Gy dedicated his life to the statistics of sampling. His fundamental law is that the sampling variance (apart from geological variance) is inversely proportional to the sample mass. Part 6: Regression Analysis for Recovery Optimization Linear
A allows the engineer to estimate main effects and interactions with minimal tests.