    \begin{align}\label{eqn: PCP_UDG}
    \mathbf{X}_U \mid \Lambda_U(s) &\sim \text{IPP}(\Lambda_U(s)), \nonumber \\
    \Lambda_U(s) \mid \mathbf{X}_c &= \sum_{j = 1}^{N_U} \text{S\'{e}rsic}(s;  \mathbf{c}_j^u, \boldsymbol{U}_j), \\
    \mathbf{X}_c &\sim \text{HPP}(\lambda_c). \nonumber
    \end{align}
