Resolution of additive mixtures into source components and contributions: A compositional approach

Methodology is developed for analysis of observations that are random linear combinations of point “source components.” Dual goals are to estimate unknown source identities and to characterize the mixing process by which sources contribute to the observations. Observations are modeled as arising from a mixture distribution, whereby the mixing component characterizes the process of interest and the kernel component captures measurement error. A parametric model is proposed, and maximum likelihood estimates of source and mixing parameters are obtained. Estimate performance is investigated by Monte Carlo simulation. Major results are devoted to studying a constraint framework within which model identifiability is guaranteed. For maximal generality, a compositional framework is applied throughout. The resolution problem discussed in this article is common in the physical sciences. For illustration, an application to air pollution data is presented.