MCMC Specifics of Latent Variable Models

We derive from analyses of several specific latent variable models an overall review of these models, under the unifying theme of their strong connections with simulation-based methods like SEm and the Gibbs sampler. We stress that the connection goes both ways, namely that these models were instrumental in designing these new methods, that the convergence properties and convergence diagnostic tools of the associated algorithms are specific to such models, and that hybrid methods like simulated maximum likelihood techniques can be proposed in such settings.