Abstract

Finite mixtures are known for modeling heterogeneity in data. The Gaussian mixture model is the most used by practitioners. The common way of estimating the parameters of this model assumes that the data is sampled through a simple random sampling process. However, in some applications such as the forensic source identification problem, data has a hierarchical structure in addition to the heterogeneity that occurs at different levels. In this work, we will discuss identifying and characterizing subpopulations when there are hierarchically structured data. This will be done through semi-supervised finite mixture models and by applying constraints that account for the hierarchy in the data. We will illustrate this based on a simulation study and a classical glass dataset. In addition, I will discuss some of the implications of this work on the forensic source identification problem.