  We show how the expectation-maximization (EM) algorithm can be applied
exactly for the fitting of mixtures of general multivariate skew t (MST)
distributions, eliminating the need for computationally expensive Monte Carlo
estimation. Finite mixtures of MST distributions have proven to be useful in
modelling heterogeneous data with asymmetric and heavy tail behaviour.
Recently, they have been exploited as an effective tool for modelling flow
cytometric data. However, without restrictions on the the characterizations of
the component skew t-distributions, Monte Carlo methods have been used to fit
these models. In this paper, we show how the EM algorithm can be implemented
for the iterative computation of the maximum likelihood estimates of the model
parameters without resorting to Monte Carlo methods for mixtures with
unrestricted MST components. The fast calculation of semi-infinite integrals on
the E-step of the EM algorithm is effected by noting that they can be put in
the form of moments of the truncated multivariate t-distribution, which
subsequently can be expressed in terms of the non-truncated form of the
t-distribution function for which fast algorithms are available. We demonstrate
the usefulness of the proposed methodology by some applications to three real
data sets.
