Assessing mixing models within a common framework

The problem of explaining a set of observations as mixtures of certain sources or end-members, occurs in many fields of science. An array of different data analysis techniques has been developed to tackle such problems within the various fields of application. Mathematically, mixing problems are similar, but the common framework is not always apparent because of the different assumptions and terminology specific to each discipline. Here, an attempt is made to present the common basis geometrically within a linear least-squares setting. The focus is on comparing and assessing models and techniques, including subjective and potentially ill-posed elements of the analysis. Careful experimental design and the use of computer experiments are recommended as part of a rational approach to mixing problems.