Accounting for model uncertainty in prediction of chlorophyll a in Lake Okeechobee

Long-term eutrophication data along with water quality measurements (total phosphorous and total nitrogen) and other physical environmental factors such as lake level (stage), water temperature, wind speed, and direction were used to develop a model to predict chlorophyll a concentrations in Lake Okeechobee. The semiparametric model included each of the potential explanatory variables as linear predictors, regression spline predictors, or product spline interactions allowing for nonlinear relationships. A Gibbs sampler was used to traverse the model space. Predictions that incorporate uncertainty about inclusion of variables and their functional forms were obtained using Bayesian model averaging (BMA) over the sampled models. Semiparametric regression with Bayesian model averaging and spline interactions provides a flexible framework for addressing the problems of nonlinearity and counterintuitive total phosphorus function estimates identified in previous statistical models. The use of regression splines allows nonlinear effects to be manifest, while their extension allows inclusion of interactions for which the mathematical form cannot be specified a priori. Prediction intervals under BMA provided better coverage for new observations than confidence intervals for ordinary least squares models obtained using backwards selection. Also, BMA was more efficient than ordinary least squares in terms of predictive mean squared error for overall lake predictions.