Frequentist and likelihood methods of inference based on the multivariate
skew-normal model encounter several technical difficulties with this model. In
spite of the popularity of this class of densities, there are no broadly
satisfactory solutions for estimation and testing problems. A general
population Monte Carlo algorithm is proposed which: 1) exploits the latent
structure stochastic representation of skew-normal random variables to provide
a full Bayesian analysis of the model and 2) accounts for the presence of
constraints in the parameter space. The proposed approach can be defined as
weakly informative, since the prior distribution approximates the actual
reference prior for the shape parameter vector. Results are compared with the
existing classical solutions and the practical implementation of the algorithm
is illustrated via a simulation study and a real data example. A generalization
to the matrix variate regression model with skew-normal error is also
presented