Application of Bayesian model and discriminant function analysis to the estimation of sediment source contributions

Abstract

Abstract Bayesian and discriminant function analysis (DFA) models have recently been used as tools to estimate sediment source contributions. Unlike existing multivariate mixing models, the accuracy of these two models remains unclear. In the current study, four well-distinguished source samples were used to create artificial mixtures to test the performance of Bayesian and DFA models. These models were tested against the Walling-Collins model, a credible model used in estimation of sediment source contributions estimation, as a reference. The artificial mixtures were divided into five groups, with each group consisting of five samples with known source percentages. The relative contributions of the sediment sources to the individual and grouped samples were calculated using each of the models. The mean absolute error (MAE) and standard error of (SE) MAE were used to test the accuracy of each model and the robustness of the optimized solutions. For the individual sediment samples, the calculated source contributions obtained with the Bayesian (MAE\xa0=\xa07.4%, SE\xa0=\xa00.6%) and Walling-Collins (MAE\xa0=\xa07.5%, SE\xa0=\xa00.7%) models produced results which were closest to the actual percentages of the source contributions to the sediment mixtures. The DFA model produced the worst estimates (MAE\xa0=\xa018.4%, SE\xa0=\xa01.4%). For the grouped sediment samples, the Walling-Collins model (MAE\xa0=\xa05.4%) was the best predictor, closely followed by the Bayesian model (MAE\xa0=\xa05.9%). The results obtained with the DFA model were similar to the values for the individual sediment samples, with the accuracy of the source contribution value being the poorest obtained with any of the models (MAE\xa0=\xa018.5%). An increase in sample size improved the accuracies of the Walling-Collins and Bayesian models, but the DFA model produced similarly inaccurate results for both the individual and grouped sediment samples. Generally, the accuracy of the Walling-Collins and Bayesian models was similar (p\xa0>\xa00.01), while there were significant differences (p