We adapt a source apportionment model from airborne particulate matter applications as a potential substitute/supplement for the current use of water pollution pathogen indicators (e.g., Coliform bacteria) at recreational beaches; the objective is to identify water-borne fecal sources for remediation to reduce exposure to disease-causing bacteria. This high-dimensional application uses fecal sterol chemical profiles from multiple sources (e.g., humans, cows, ducks, etc.); therefore, we use a Hamiltonian Markov chain Monte Carlo method to sample the parameters efficiently and attribute the percentage contribution of potential fecal bacterial sources from the composite mixtures. We then compare this approach with other source apportionment approaches currently in use.
Results/Conclusions
We use a laboratory data set of 39 contrived ‘mixtures’ for eight sterols and four fecal sources that controlled the source allocations and measured sterols in the composites. Using sterol profiles and non-informative source contribution estimates as priors, we infer the source allocations (and their profiles) from the observed chemical data. The majority of simulated mixtures demonstrate substantial agreement with the initial conditions of the experimental combinations. A model selection approach is also implemented, Kullbach-Leibler divergence, to quantify model performance. Using this metric, the Hamiltonian MCMC approach outperforms both a null model maximum entropy approach and a deterministic least squares method.
