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Title: On mixture modelling with multivariate skew distributions Authors:  Sharon Lee - University of Queensland (Australia)
Geoffrey McLachlan - University of Queensland (Australia) [presenting]
Abstract: In recent years, there has been increasing use of non-normal distributions in the modelling and analysis of heterogeneous data. Attention is focussed on the use of skew symmetric distributions with multivariate skewing functions that allow for the modelling of skewness in $p$ arbitrary directions in the feature space, where $p$ is the number of variables. In particular, various multivariate skew normal and skew $t$- distributions are considered corresponding to some commonly used characterizations in the literature. Parameter estimation for these distributions and mixtures of them can be obtained via the Expectation-Maximization (EM) algorithm. However, the E-step for such models typically involves the calculation of multidimensional integrals that are computationally expensive to evaluate. Some approaches are therefore considered to reduce the computation time required for the fitting of these models. In addition to methods that are directly applicable to single-threaded implementation, an approach is developed that utilizes the processing resources available from machines with multiple cores. An example on a real dataset will be given to illustrate the approach.