Posterior Inference in the Random Intercept Model Based on Samples Obtained with Markov Chain Monte Carlo Methods

Many papers (including most of the papers in this issue of Computational Statistics) deal with Markov Chain Monte Carlo (MCMC) methods. This paper will give an introduction to the augmented Gibbs sampler (a special case of MCMC), illustrated using the random intercept model. A 'nonstandard' application of the augmented Gibbs sampler will be discussed to give an illustration of the power of MCMC methods. Furhtermore, it will be illustrated that the posterior sample resulting from an application of MCMC can be used for more than determination of convergence and the computation of simple estimators like the a posteriori expetation and standard deviation. Posterior samples give access to many other inferential possibilities. Using a simulation study, the frequency properties of some of these possibilities will be evaluated