ON A MULTIVARIATE IMPLEMENTATION OF THE GIBBS SAMPLER

It is well established that when the parameters in a model are correla ted, the rate of convergence of Gibbs chains to the appropriate statio nary distributions is faster and Monte-Carlo variances of features of these distributions are lower for a given chain length, when the Gibbs sampler is implemented by blocking the correlated parameters and samp ling from the respective conditional posterior distributions takes pla ce in a multivariate rather than in a scalar fashion. This block sampl ing strategy often requires knowledge of the inverse of large matrices . In this note a block sampling strategy is implemented which circumve nts the use of these inverses. The algorithm applies in tile context o f the Gaussian model and is illustrated with a small simulated data se t.