  In this paper we take up Bayesian inference in general multivariate stable
distributions. We exploit the representation of Matsui and Takemura (2009) for
univariate projections, and the representation of the distributions in terms of
their spectral measure. We present efficient MCMC schemes to perform the
computations when the spectral measure is approximated discretely or, as we
propose, by a normal distribution. Appropriate latent variables are introduced
to implement MCMC. In relation to the discrete approximation, we propose
efficient computational schemes based on the characteristic function.
