Dirichlet based Bayesian multivariate receptor modeling

We propose a simple, fully Bayesian approach for multivariate receptor modeling that allows for flexible and consistent incorporation of a priori information. The model uses a generalization of the Dirichlet distribution as the prior distribution on source profiles that allows great flexibility in the specification of prior information. Heavy-tailed lognormal distributions are used as priors on source contributions to match the nature of particulate concentrations. A simulation study based on the Washington, DC airshed shows that the model compares favorably to Positive Matrix Factorization, a standard analysis approach used for pollution source apportionment. A significant advantage of the proposed approach compared to most popularly used methods is that the Bayesian framework yields complete distributional results for each parameter of interest (including distributions for each element of the source profile and source contribution matrices). These distributions offer a great deal of power and versatility when addressing complex questions of interest to the researcher.