\begin{align}
f(y_{i}^{(p)}, z_{i}^{(p)}) &= \sum_{j \in J} \sum_{\ell \in L} \boldsymbol\beta_{j\ell} \cdot \textrm{TruncNorm}(\mathbf{m}_j, \lambda_\ell \mathbf{S}_j). \\
\boldsymbol\beta &\sim \text {Symmetric-Dirichlet}_{(J\times L)}(\alpha = 1/2)    
\end{align}
