Bayesian methods for regional-scale eutrophication models.

We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amount of data available and (3) be flexible enough to permit updates and improvements. Tree-based methods are a flexible approach useful for variable subset selection and when the analyst suspects global nonlinearity and cannot (or does not want to) specify the functional form of possible interactions a priori. We use the US EPA National Eutrophication Survey data to fit three models demonstrating the methods and to highlight important differences arising from slightly different model specifications. The Bayesian approach offers many advantages, including the estimation of the value of new information and proper probability distributions on the variable of interest as an output, which can be directly used in risk assessment or decision-making.