Fig. 1

An example hierarchical model where the parameter \(\theta _i\) describes the probability distribution of the outcome \(y_i\) for subject i. In this graphical model, an arrow from a to b indicates that b is generated via a through a distribution \(p_{a} (b)\), or in other words, a describes the distribution of b. The main part of this hierarchical model is that \(\theta _i\)’s are themselves assumed to be draws from a common distribution described by a hyperparameter \(\phi\), which within a Bayesian framework, has its own prior distribution