Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 96, Issue 456, Pages 1184-1193Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/016214501753381832
Keywords
Bayesian analysis; cross validation; hierarchical model; Markov chain Monte Carlo; prediction
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We develop a Bayesian hierarchical model linking arsenic concentrations in the source waters of U.S. community water systems to system characteristics such as source water type and location. This characterization provides a starting point for the assessment of current and required water treatment to meet proposed maximum contaminant level (MCL) standards. After a model validation study based on predictive densities, we use a national census of treatment systems and their associated covariates to predict the national distribution of raw water arsenic concentrations. We then examine the relationship between alternative MCLs and the number of systems requiring treatment modification and identify classes of systems which are most likely to be problematic. The posterior distribution of the model parameters, obtained using Markov Chain-Monte Carlo (MCMC), quantifies the uncertainty in model predictions. We use this quantification to designate classes of water systems where future sampling would most substantially reduce uncertainties in national estimates of arsenic occurrence.
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