An interval estimator for the unmixing of mixtures with set-based source descriptions

• We propose an interval estimator for the proportional contribution of a source (or ingredient) to a mixture.
• Sources (or ingredients) can be represented by means of sets.
• We present a computationally tractable optimization problem to compute an interval estimate in practice.

The unmixing of mixtures, i.e., the computation of the proportional contribution of a set of sources to a mixture, is of interest to a multitude of applied research disciplines. We consider an unmixing problem in which a mixture is represented by a point in RnRn, and the sources are represented by subsets of RnRn. We argue that the proportional contribution of a source of interest to that mixture can naturally be estimated by an interval estimator, as opposed to a more traditional point estimator. An interval estimator is proposed and it is shown that this estimator can be computed efficiently in a variety of cases by solving an optimization problem.