\begin{align*}
    \mathbf{X} \mid \Lambda &\sim \text{IPP}(\Lambda(s)), \\
    \Lambda(s)\mid \mathbf{X}_c, \boldsymbol{\Xi} &= \beta_0 + \sum_{k=1}^{N_G}\text{S\'{e}rsic}(s;  c_k, \boldsymbol{G}_k) + \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).
\end{align*}
