Convergence Control of MCMC Algorithms

There is an obvious difference between the theoretical guarantee that f is the stationary distribution of a Markov chain (x(t)) and the practical requirement that (1.2) is close enough to (1.1). It is thus necessary to develop diagnostic tools towards the latter goal, namely convergence control.1While control is the topic of this book, we first present in this chapter some of the usual methods, before embarking upon the description of new control methods. The reader is referred to the survey papers of Brooks (1998), Brooks and Roberts (1998) and Cowles and Carlin (1996), as well as to Robert and Casella (1998) and Gelfand and Smith (1998) for details.