Application of the hierarchical Bayesian models to analyze semi-autogenous mill throughput

• The aim is to provide a robust statistical framework for improving process control strategies in SAG milling operations. • Bayesian Hierarchical Models capture the causalities between geological and operational variables for SAG mill throughput. • The hierarchical framework accounts for nested data structures, enabling partial pooling of information across campaigns. • This research also detects causal inference in SAG mill performance. Optimizing throughput in semi-autogenous grinding (SAG) mills is a critical challenge in mining and mineral processing, directly influencing energy efficiency and operational costs. While mill speed, power, dimensions, ball charge, and feed rate can be controlled, uncertainties in ore hardness, particle size distribution, and liner wear create significant variability in performance. These challenges necessitate a modeling approach that not only captures operational dependencies but also accounts for hierarchical data structures and uncertainty. This study employs a Bayesian Hierarchical Model (BHM) to quantify the relationships between geological, blasting, and mill operational factors, providing a structured probabilistic framework for throughput prediction and decision-making. A systematic variable selection process using Bayesian inference identifies ore hardness, SAG mill rotation speed (RPM), and the tonnage of crushed material as the most influential predictors. The model also accounts for liner wear across multiple operational liner age periods, capturing its cumulative effect on power consumption and grinding efficiency. Unlike conventional statistical techniques, which assume fixed variable relationships, the Bayesian approach allows partial pooling across operational contexts, improving predictive accuracy and adaptability. The findings highlight the advantages of Bayesian methods over traditional regression techniques through uncertainty quantification and hierarchical structure. Integrating domain knowledge with probabilistic modeling enhances SAG mill prediction, enabling data-driven decision-making in complex mining environments. The results provide a foundation for improving energy efficiency, reducing operational variability, and refining throughput predictions under diverse geological and equipment conditions. This study advances statistical methodologies in mining process optimization, demonstrating the practical benefits of Bayesian modeling in industrial applications.