Graphical models are frequently used to model dependencies in large, complex stochastic systems. Bayesians often use them to characterize propagation of learning in expert systems. Also, the properties of directed acyclic graphs greatly simplify the derivations of full conditionals in Gibbs sampling schemes. In this paper we use them to clarify and simplify usual analytical computations in Bayesian hierarchical models. The scenario is that of designing and analyzing the replication of a performed experiment.

Keywords: Acceptance-rejection Metropolis-Hastings algorithm; Bayesian hierarchical models; Exact replications; Non-central t; Prediction; Stochastic EM algorithm.