Estimation for finite mixture of simplex models: applications to biomedical data

Simplex distribution has been proved useful for modelling double-bounded variables in data directly. Yet, it is not sufficient for multimodal distributions. This article addresses the problem of estimating a density when data is restricted to the (0,1) interval and contains several modes. Particularly, we propose a simplex mixture model approach to model this kind of data. In order to estimate the parameters of the model, an Expectation Maximization (EM) algorithm is developed. The parameter estimation performance is evaluated through simulation studies. Models are explored using two real datasets: i) gene expressions data of patients’ survival times and the relation to adenocarcinoma and ii) magnetic resonant images (MRI) with a view in segmentation. In the latter case, given that data contains zeros, the main model is modified to consider the zero-inflated setting.