Multivariate Receptor Models and Model Uncertainty

Estimation of the number of major pollution sources, the source composition profiles, and the source contributions is the main interest in multivariate receptor modeling. Due to lack of identifiability of the receptor model, however, the estimation cannot be done without some additional assumptions. A common approach to this problem is to estimate the number of sources, q, at the first stage, and then estimate source profiles and contributions at the second stage, given additional constraints (identifiability conditions) to prevent source rotation/transformation and the assumption that the q-source-model is correct. These assumptions on the parameters (the number of sources and identifiability conditions) are the main source of model uncertainty in multivariate receptor modeling. In this paper, we suggest a Bayesian approach to deal with model uncertainties in multivariate receptor models by using Markov chain Monte Carlo (MCMC) schemes. Specifically, we suggest a method which can simultaneously estimate parameters (compositions and contributions), parameter uncertainties, and model uncertainties (number of sources and identifiability conditions). Simulation results and an application to air pollution data are presented.