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Frequentist and likelihood methods of inference based on the multivariateskew-normal model encounter several technical difficulties with this model. Inspite of the popularity of this class of densities, there are no broadlysatisfactory solutions for estimation and testing problems. A generalpopulation Monte Carlo algorithm is proposed which: 1) exploits the latentstructure stochastic representation of skew-normal random variables to providea full Bayesian analysis of the model and 2) accounts for the presence ofconstraints in the parameter space. The proposed approach can be defined asweakly informative, since the prior distribution approximates the actualreference prior for the shape parameter vector. Results are compared with theexisting classical solutions and the practical implementation of the algorithmis illustrated via a simulation study and a real data example. A generalizationto the matrix variate regression model with skew-normal error is alsopresented.

Bayesian inference for the multivariate skew-normal model: a Population Monte Carlo approach