Chemical mass balance when an unknown source exists

A chemical mass balance method is proposed for the case where the existence of an unknown source is suspected. In general, when the existence of an unknown source is assumed in statistical receptor modeling, unknown quantities such as the composition of an unknown source and the contributions of assumed sources become unidentifiable. To estimate these unknown quantities avoiding the identification problem, a Bayes model for chemical mass balance is constructed in the form of composition without using prior knowledge on the unknown quantities except for natural constraints. The covariance of ambient observations given in the form of composition is defined in several ways. Markov chain Monte Carlo is used for evaluating the posterior means and variances of the unknown quantities as well as the likelihood for the proposed model. The likelihood is used for selecting the best fit covariance model. A simulation study is carried out to check the performance of the proposed method.