  We are thankful to the discussants for their hard, interesting work. The main
purpose of our paper was to give reasonably sharp rates of convergence for some
simple examples of the Gibbs sampler. We chose examples from expository
accounts where direct use of available techniques gave practically useless
answers. Careful treatment of these simple examples grew into bivariate
modeling and Lancaster families. Since bounding rates of convergence is our
primary focus, let us begin there. [arXiv:0808.3852]
