A hierarchical modeling approach for estimating national distributions of chemicals in public drinking water systems

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 occurring in U.S. public drinking water systems using fluoride and thallium as examples. 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, was evaluated using simulated data sets generated from a series of Weibull distributions to illustrate the robustness of the model. The hierarchical model is easily implemented using the Markov chain Monte Carlo simulation method. In addition, the Bayesian method is able to quantify the uncertainty in the estimated cumulative density function. The estimated fluoride and thallium national distributions are presented. Results from this study can be used to develop prior distributions for future U.S. drinking water regulatory studies of contaminant occurrence.