Gibbs sampling is a technique to calculate a complex posterior distribution as steady state measure of a Markov chain. The fundamental problem of inference from Markov chain simulation is that there will always be areas of the target distribution that have not been covered by the finite chain. Deciding when to stop the chain in order to have reached enough coverage of the support of the target distribution is an important matter. Techniques based on one long single chain and on multiple chains are discussed in the framework of a linear mixed effects model. The diagnostics used do not provide a consistent view on the convergence. Practical consequences on the estimates are shown.
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