A Hierarchical Modelling Approach for Estimating National Distributions of Chemicals in Public Drinking Water Systems: A Case Study of Fluoride

Water quality studies often include the analytical challenge of incorporating censored data and quantifying error of estimation. Many analytical methods exist for estimating distribution parameters when censored data are present. This paper presents a Bayesian-based hierarchical model for estimating the national distribution of the mean concentrations of chemicals in US public drinking water systems using fluoride as an example. The data used are Safe Drinking Water Act compliance monitoring data (with a significant proportion of left-censored data). The model, which assumes log-normality of the fluoride concentration data, was evaluated using simulated data sets generated from a series of Weibull distributions to illustrate the robustness of the model. When compared to the regression on ordered statistics (ROS) method (another modelling approach for censored data), the Bayesian model tracks the true distribution well, while the ROS plotting position method yielded a distribution with a slightly larger variance and smaller median. In addition, the Bayesian method is able to quantify the uncertainty in the estimated cumulative density function. The estimated fluoride national distribution is presented. Key Terms: Bayesian statistics, Fluoride, left-censored data, MCMC, risk, Safe Drinking Water Act Joint Statistical Meetings Section on Statistics & the Environment