For the applied statistician, data augmentation is a powerful tool for solving optimization problems. In this thesis, I address a problem in some data augmented Gibbs samplers. I show that although...Show moreFor the applied statistician, data augmentation is a powerful tool for solving optimization problems. In this thesis, I address a problem in some data augmented Gibbs samplers. I show that although introducing latent variables renders a sampling problem tractable, this comes at the price of raising the autocorrelation of the Markov chain, as the number of parameters increases, in this case the number of items in a test. By means of an example, I show that data augmentation is a powerful yet inefficient tool in cases of increased number of items, since the autocorrelation (and hence the rate of the convergence) of the addressed augmented Gibbs sampler is proved to be dependent on the number of item parameters. We wish to show that although most data-augmented samplers are well behaved, in this example the algorithm becomes really slow and faces the possibility of grinding to a haltShow less