Bayesian quantile multivariate receptor modeling

Multivariate receptor modeling is a collection of methods used for identifying major pollution sources and estimating their impacts by resolving ambient measurements of air pollutants collected at a receptor (or receptors) into components associated with different sources of air pollution. Air pollution data are often right-skewed and contain several outliers. While the outliers resulting from a laboratory error or a contamination in the field are considered to be faulty observations and need to be removed, some outliers such as those resulting from extreme values in source contributions may be valid observations and convey important information. In some cases, the modeling of very high concentrations of air pollutants such as 95th percentiles or 99th percentiles and estimating the corresponding source contributions and compositions, which could be different from those for the mean concentrations, may be of specific interest, e.g., in setting the standards for pollution control. Thus, it would be beneficial to model both the center and the tails of the distribution of air pollution data so that source contributions for extreme observations as well as those for typical observations can be estimated in order to provide more comprehensive knowledge on air pollution and underlying sources. In this paper, we propose a new flexible source apportionment approach, Bayesian quantile multivariate receptor modeling, which can easily deal with the non-normality of air pollution data and outliers by extending the idea of quantile regression. Bayesian quantile multivariate receptor modeling can estimate the source contributions corresponding to any part of the data distribution including the tails and the center. It can also be easily implemented by JAGS, free software developed for the analysis of Bayesian models using the Markov chain Monte Carlo simulation. The proposed method is illustrated with simulated data and PM_2.5 speciation data from El Paso, Texas, USA.