This chapter revisits the theoretical basis for Markov chain Monte Carlo but with greater

detail and more attention to issues of convergence. Most of the technical content is intended

to give a greater appreciation for the underlying mathematical process of Markov chains and

therefore an understanding of the issues involved in convergence and mixing. Both conver-

gence and mixing behavior of Markov chains affect the final inferences made with Bayesian

models using MCMC. Readers who wish to move onto more practical considerations can

proceed to Chapter 14 and return to this information as needed.