an class="math inline">\(\boldsymbol{U} \in \mathbb{S}_d\)</span> follows a
<span class="math inline">\(d\)</span>-mixture of Dirichlet with the
<span class="math inline">\(j\)</span>th component being <span class="math inline">\(\mathcal{D}(\boldsymbol{1}-\delta_{j}\alpha_j)\)</span>,
so that the mixture has density function <span class="math display">\[\begin{align*}
h_{\boldsymbol{U}}(\boldsymbol{u})=\frac{1}{d} \sum_{j=1}^d
\frac{\Gamma(d-\alpha_j)}{\Gamma(1-\alpha_j)} u_j^{-\alpha_j}
\end{align*}\]</sp