| Summary: | Utilizing Bayesian hierarchical techniques, regional-scale eutrophication models were developed for use in the Total Maximum Daily Load (TMDL) process. The Bayesian tree-based (BTREED) approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the water quality model. Simple parametric models are often inadequate for describing complex datasets; the BTREED approach partitions the dataset, and describes the localized subsets of data with linear models, thereby providing a comprehensive representation of stressor and response interactions. Nutrient criteria data for lakes, ponds and reservoirs across the United States were obtained from the Environmental Protection Agency (U.S. EPA) National Nutrient Criteria Database. Model estimation was accomplished by randomly splitting the composite dataset into training and test sets, and using the training dataset in model estimation, and the test dataset to evaluate and validate the model. Mean squared error was reported for both training and test data of the highest log-likelihood models. The Bayesian approach to regional-scale eutrophication models is also beneficial from a decision-theoretic perspective. Predictions regarding the variable of interest are quantified by probability distributions, providing the decision maker with valuable information about the distribution of the biological response conditional on the stressors, and information about the model error.
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