 Solution

For each $i$, place ${\xi }_i$ and ${\eta }_i$ inside a plate replicated $N$ times. The directed edges are represented byThe shaded observed nodes are $x_i,y_i$; the unshaded nodes ${\xi }_i,{\eta }_i$ are latent; and $\alpha ,\beta ,{\sigma }^2,\mu ,{\tau }^2$ lie outside the plate. This is the probabilistic graphical model encoded by the joint factorization.