Robust mixture modeling using multivariate skew t distributions

Abstract

This paper presents a robust mixture modeling framework using the multivariate skew t distributions, an extension of the multivariate Student's t family with additional shape parameters to regulate skewness. The proposed model results in a very complicated likelihood. Two variants of Monte Carlo EM algorithms are developed to carry out maximum likelihood estimation of mixture parameters. In addition, we offer a general information-based method for obtaining the asymptotic covariance matrix of maximum likelihood estimates. Some practical issues including the selection of starting values as well as the stopping criterion are also discussed. The proposed methodology is applied to a subset of the Australian Institute of Sport data for illustration.

Parametric modeling of cellular state transitions as measured with flow cytometry

“…By design, our STNMIX model is computationally faster to fit than the skew t mixture (STMIX) model [3,12,16,17] without sacrificing precision or rigor. Ho et al [13] summarized the differences between the STMIX and STNMIX models and showed the implementation of the STNMIX model is generally much simpler and faster than that of STMIX model.…”

Model-Based Clustering

“…Extensive details on skew-normal and skew-t distributions are given by Azzalini and Capitanio (2014). Mixtures of these formulations have been used for clustering and classification in several contexts, including work by Lin (2009Lin ( , 2010, McNicholas (2012, 2014), and McLachlan (2013a,b, 2014). Vrbik and McNicholas (2014) introduce skew-normal and skew-t analogues of the GPCM family and show that they can give superior clustering and classification performance when compared with their Gaussian counterparts.…”

A matrix variate skew‐t distribution

“…For example, some work has been done using symmetric component densities that parameterize concentration (tail weight), e.g., the t distribution , Andrews & McNicholas 2011, Lin, McNicholas & Hsiu 2014) and the power exponential distribution (Dang, Browne & McNicholas 2015). There has also been work on mixtures for discrete data (e.g., Karlis & Meligkotsidou 2007, Bouguila & ElGuebaly 2009) as well as several examples of mixtures of skewed distributions such as the NIG distribution (Karlis & Santourian 2009, Subedi & McNicholas 2014, the skew-t distribution (Lin 2010, Vrbik & McNicholas 2012, Lee & McLachlan 2014, 2016, the shifted asymmetric Laplace distribution (Morris & McNicholas 2013, Franczak, Browne & McNicholas 2014, the variance-gamma distribution , the generalized hyperbolic distribution , and others (e.g., Elguebaly & Bouguila 2015, Franczak, Tortora, Browne & McNicholas 2015.…”