A system to test for convergence of the Gibbs sampler

A computational technique which has gained a lot of popularity in the Bayesian community in recent years is that of Markov Chain Monte Carlo methods. The Gibbs Sampler is among the most widely used of these methods due, in a large part, to its simplicity. One of the major problems with this and many other forms of MCMC is in knowing when enough iterations have been completed for us to be confident in the accuracy of Monte Carlo inferences on the output of the algorithm. Many attempts at answering this question have been proposed in the last few years and in this thesis I shall look at some of these methods. I shall also propose a new diagnostic which performs very well in examples. These examples include models which are known to exhibit slow convergence and characteristics that cause problems for many existing convergence diagnostics. The new diagnostic has the advantage of being determined quantitatively and so the task of deciding whether the Markov chains have reached their stationary state or not can be fully automated.