Solution
= Solution
For one object, the <probabilistic graphical model> factorization is
$$
\boxed{
p(x_i,y_i,\xi_i,\eta_i\mid\alpha,\beta,\sigma^2,\mu,\tau^2)
=p(x_i\mid\xi_i)p(y_i\mid\eta_i)
p(\eta_i\mid\xi_i,\alpha,\beta,\sigma^2)
p(\xi_i\mid\mu,\tau^2).}
$$
Each factor is the <normal distribution> density specified by the model. This factorization displays the <conditional independences> of the <latent variables> $\xi_i,\eta_i$ and the noisy observations $x_i,y_i$.