On the Geometrical Convergence of Gibbs Sampler inRd

The geometrical convergence of the Gibbs sampler for simulating a probability distribution inRdis proved. The distribution has a density which is a bounded perturbation of a log-concave function and satisfies some growth conditions. The analysis is based on a representation of the Gibbs sampler and some powerful results from the theory of Harris recurrent Markov chains.