Machine Learning and Bayesian Approaches for Concrete Compressive Strength Prediction: A Comparative Study Using the UCI Dataset

<title>Abstract</title> <p>The increasing complexity of modern concrete mixtures, driven by sustainability imperatives and performance requirements, has exposed the limitations of traditional empirical mix design methods. This paper presents a comprehensive review and computational analysis of Bayesian statistical methods applied to concrete mix design using the UCI Machine Learning Repository’s Concrete Compressive Strength dataset (1,030 observations with 8 input variables). Our analysis implements multiple approaches including Gaussian process regression (GPR), random forest, XGBoost with Bayesian optimization, hierarchical Bayesian modeling, Monte Carlo simulation, and sensitivity analysis. The computational results demonstrate that XGBoost achieves the best performance with R² = 0.919 and RMSE = 4.69 MPa on test data, followed by Random Forest (R² = 0.869, RMSE = 5.96 MPa). For Gaussian Process Regression, we evaluated three configurations: default GPR with automatic sigma estimation (R² = 0.794, RMSE = 7.47 MPa), optimized GPR with cross-validated sigma selection (R² = 0.797, RMSE = 7.41 MPa), and fixed-sigma GPR (R² = 0.758, RMSE = 8.10 MPa). While GPR hyperparameter tuning yields only incremental improvements (0.8% RMSE reduction), tree-based ensemble methods substantially outperform GPR on this dataset. Hierarchical variance decomposition reveals substantial variability in concrete strength across age groups, with the 15-28 day group containing the most observations (41.3% of the data). Bayesian optimization for XGBoost hyperparameter tuning achieves a validation RMSE of approximately 3.84 MPa after 15 iterations. Monte Carlo simulation provides prob-abilistic strength predictions with a characteristic strength (5th percentile) of 30.8 MPa for typical mix designs. Sensitivity analysis identifies water-to-binder ratio as the dominant factor influencing concrete strength. This comprehensive analysis demonstrates that while machine learning methods like XGBoost offer superior predictive accuracy, GPR provides the unique advantage of providing full predictive distributions with uncertainty quantification. To facilitate practical adoption, all R codes and an interactive R Shiny application have been made publicly available, enabling users to analyze their own concrete mix design data.</p>