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.
| | Description | Statistical Solution(s) | | :--- | :--- | :--- | | Data Clustering | Drill holes are not uniformly distributed, leading to over-representation of densely sampled areas. | Declustering : Assigning lower weights to samples in high-density clusters to ensure the global histogram is unbiased. | | Skewed Distributions | Ore grades typically follow a lognormal distribution, violating normality assumptions. | Data Transformation : Applying log, normal-score, or logratio transformations to achieve a more Gaussian distribution. | | High Nugget Effect | A large nugget effect indicates high variability at a small scale, often linked to ore texture. | Non-Linear Geostatistics : Using methods like Indicator Kriging or Gaussian anamorphosis to handle high variability and skewed distributions. | | Multivariate Relationships | Valuing an orebody often involves multiple correlated variables (e.g., copper & molybdenum). | Multivariate Geostatistics : Using cross-variograms and Co-Kriging to estimate a primary variable from a more densely sampled secondary variable. |
Ore bodies and processing streams are governed by specific statistical distributions. Recognizing these patterns allows engineers to predict system behavior accurately. Normal (Gaussian) Distribution
Arises from spatial heterogeneity, such as heavier minerals settling to the bottom of a conveyor belt or slurry launder. Statistical Methods For Mineral Engineers
) requires 8 distinct runs and maps all main effects and interaction terms. Fractional Factorial Designs ( 2k−p2 raised to the k minus p power
Measures how many standard deviations a data point is from the mean. Points with a are typically flagged for review. Interquartile Range (IQR): Data falling outside
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. Pierre Gy dedicated his life to the statistics of sampling
Compares means across three or more groups simultaneously. For example, ANOVA can determine if three different blast patterns yield significantly different semi-autogenous grinding (SAG) mill throughput rates.
Statistical methods are indispensable for modern mineral engineering. By utilizing data analysis, experimental design, and optimization methods, engineers can better understand the complexities of mineral processing, reduce uncertainty, and maximize efficiency in mining operations.
Subject to the constraint that mass must be conserved across all nodes. This optimization dampens the effect of noisy, unreliable measurements while trusting highly accurate instruments. 6. Advanced Multivariate Statistics and Machine Learning | Declustering : Assigning lower weights to samples
6. Design of Experiments (DoE) and Response Surface Methodology
: Using tools like t-tests and F-tests to compare different operating regimes.
): Failing to detect a real process improvement (false negative). 4. Empirical Modeling: Regression and Correlation
Statistical methods are no longer optional tools for the modern mineral engineer; they are fundamental to survival in a low-grade, high-cost mining landscape. By systematically applying descriptive statistics, sampling theory, hypothesis testing, DoE, and data reconciliation, operations can reduce process variance, optimize chemical consumption, maximize metallurgical recovery, and ultimately improve the bottom line of the operation.
Batch flotation testing is standard to assess ore response to new reagents or grinding media. Statistical methods are crucial to: