2012/11/22 by Sharon Lee, Geoffrey J. McLachlan, Lee, Sharon X. +1 · 1 citation
Computer Science · Environmental Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Hydrology and Drought Analysis #Methodology (stat.ME) #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1211.5290
openalex publication_date 2012/11/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
This paper describes an algorithm for fitting finite mixtures of unrestricted Multivariate Skew t (FM-uMST) distributions. The package EMMIX-uskew implements a closed-form expectation-maximization (EM) algorithm for computing the maximum likelihood (ML) estimates of the parameters for the (unrestricted) FM-MST model in R. EMMIX-uskew also supports visualization of fitted contours in two and three dimensions, and random sample generation from a specified FM-uMST distribution. Finite mixtures of skew t-distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour, for example, datasets from flow cytometry. In recent years, various versions of mixtures with multivariate skew t (MST) distributions have been proposed. However, these models adopted some restricted characterizations of the component MST distributions so that the E-step of the EM algorithm can be evaluated in closed form. This paper focuses on mixtures with unrestricted MST components, and describes an iterative algorithm for the computation of the ML estimates of its model parameters. The usefulness of the proposed algorithm is demonstrated in three applications to real data sets. The first example illustrates the use of the main function fmmst in the package by fitting a MST distribution to a bivariate unimodal flow cytometric sample. The second example fits a mixture of MST distributions to the Australian Institute of Sport (AIS) data, and demonstrate that EMMIX-uskew can provide better clustering results than mixtures with restricted MST components. In the third example, EMMIX-uskew is applied to classify cells in a trivariate flow cytometric dataset. Comparisons with other available methods suggests that the EMMIX-uskew result achieved a lower misclassification rate with respect to the labels given by benchmark gating analysis.