Markov chain Monte Carlo (MCMC) methods have become a popular approach to statistical inference when the probability distributions of interest are 
intractable.  The objective of these methods is to simulate a sequence of data from which we can draw inferences about the ``truth''.  Under certain 
conditions, a central limit theorem will exist for the Markov chain.  In this case, we can use consistent estimators of the corresponding asymptotic 
variance to provide guidance on how long we need to run the chain so that the resulting estimates are sufficiently accurate.  We will discuss the conditions 
required for the existence of a central limit theorem and how these conditions are established in practice.  Ultimately, we show that a central limit theorem 
exists for a block Gibbs sampler for a Bayesian version of the random intercepts model.