Bayesian linear regression with Gaussian mixture likelihood for outlier detection of metal grades in Porphyry Cu deposit
Bibliographic record
Abstract
Metal grade, as a critical property, is used during mineral exploration, ore sorting and mineral processing. Geochemical bore core data is the primary source of determining pay and deleterious metal grades. The pay metal grade receives more attention than the deleterious metal grade due to its economic value in determining the profitability and viability of mining projects. However, estimating deleterious metal grades is also crucial for optimising mine planning, ore sorting, stockpiling, and mineral processing. Metal grade usually contains extrema, or “outliers” due to measurement error, latent geological features, and spatial heterogeneity of mineral distribution. The outliers of deleterious metal grades can produce significant regression bias as the outliers are overweighted in traditional regression model. This will further complicate decision-making for ore sorting optimisation and mineral processing resulting in excessive chemical dosage, water, and energy expense. We present a Bayesian linear regression model with Gaussian mixture likelihood (BLR-GML) to identify deleterious Fe grade outliers in the relationship with pay metals of Cu in a porphyry Cu deposit. Results show that the BLR-GML model dramatically reduces mean square error and provide more accurate inference than maximum likelihood estimation. We also illustrate how outliers are crucial during mine planning and can be used as a cost function when selecting block size and orientation. BLR-GML model offers a reliable way to capture outliers in the linear relationship of metal grades. This is particularly valuable for mineral inference that supports decision-making through the minerals value chain and our goal of sustainable metal supply.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".