  We propose a novel set of Poisson Cluster Process (PCP) models to detect
Ultra-Diffuse Galaxies (UDGs), a class of extremely faint, enigmatic galaxies
of substantial interest in modern astrophysics. We model the unobserved UDG
locations as parent points in a PCP, and infer their positions based on the
observed spatial point patterns of their old star cluster systems. Many UDGs
have somewhere from a few to hundreds of these old star clusters, which we
treat as offspring points in our models. We also present a new framework to
construct a marked PCP model using the marks of star clusters. The marked PCP
model may enhance the detection of UDGs and offers broad applicability to
problems in other disciplines. To assess the overall model performance, we
design an innovative assessment tool for spatial prediction problems where only
point-referenced ground truth is available, overcoming the limitation of
standard ROC analyses where spatial Boolean reference maps are required. We
construct a bespoke blocked Gibbs adaptive spatial birth-death-move MCMC
algorithm to infer the locations of UDGs using real data from a \textit{Hubble
Space Telescope} imaging survey. Based on our performance assessment tool, our
novel models significantly outperform existing approaches using the
Log-Gaussian Cox Process. We also obtained preliminary evidence that the marked
PCP model improves UDG detection performance compared to the model without
marks. Furthermore, we find evidence of a potential new ``dark galaxy'' that
was not detected by previous methods.
