Bayesian inference for the multivariate skew-normal model: A population Monte Carlo approach

Frequentist and likelihood based methods of inference encounter several difficulties with the multivariate skew-normal model. In spite of the popularity of this class of densities, there are no broadly satisfactory solutions for estimation and testing problems. In this paper we propose a general population Monte Carlo algorithm which exploits the stochastic representation of the skew-normal random variables in terms of latent structure to provide a full Bayesian analysis of the model. Our approach can be defined weakly informative since we use priors which approximate the actual reference prior for the shape parameter vector. We compare our results with the existing classical solutions and illustrate the practical implementation of the algorithm.