Bayesian linear regression with Gaussian mixture likelihood for outlier
detection of metal grades in Porphyry Cu deposit
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.