 + \tau_w^2 + \text{se}_1^2 &amp; \tau_w^2 &amp; \dots &amp; \tau_w^2  \\
      \tau_w^2 &amp; \tau_b^2 + \tau_w^2 + \text{se}_2^2 &amp; \dots &amp; \tau_w^2  \\
      \dots  &amp; \dots &amp; \dots &amp; \dots \\
      \tau_w^2 &amp; \tau_w^2 &amp; \dots &amp; \tau_b^2 + \tau_w^2 + \text{se}_{J_k}^2 &amp; \\
  \end{bmatrix}.
\end{aligned}
</annotation></semantics></math> The random effects marginalization is
helpful as it allows us to sample fewer parameters from the posterior
distribution (which significa