Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 44 / 2 / a / Solution

The Bayesian network has a shared parent $\psi$ and, for each hospital, the chain $\psi \to {\theta }_i\to y_i$. A plate encloses the hospital-specific pair. Observed counts are shaded; the local rates are latent variables. Conditional on $\psi$, the pairs are independent.