Simulation of compound hierarchical models

Hierarchical probability models are widely used for data classified in a treelike structure and in Bayesian inference. The main characteristic of such models is to have the probability law at some level in the classification structure be conditional on the outcome in previous levels. For example, adopting a bottom to top description of the model, a simple hierarchical model could be written as Xt|Λ,Θ ∼ Poisson(Λ) Λ|Θ ∼ Gamma(3,Θ) Θ ∼ Gamma(2,2), (1)