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.

翻译：我们提出了一组新颖的泊松簇过程（PCP）模型，用于探测超弥散星系（UDGs）——一类在现代天体物理学中具有重要研究价值的极其暗淡且充满谜团的星系。我们将未观测到的UDG位置建模为PCP中的母点，并根据其古老星团系统的观测空间点模式推断这些位置。许多UDG拥有从数个到数百个这类古老星团，我们在模型中将其视为子点。此外，我们提出了一种新框架，利用星团的标记构建带标记的PCP模型。带标记的PCP模型可增强UDG的探测能力，并为其他学科的问题提供广泛适用性。为评估整体模型性能，我们设计了一种创新的空间预测问题评估工具，此类问题中仅存在点参考的真实数据，从而克服了标准ROC分析需要空间布尔参考图的局限性。我们构建了定制的分块吉布斯自适应空间生灭移动马尔可夫链蒙特卡洛（MCMC）算法，利用哈勃空间望远镜成像巡天的真实数据推断UDG的位置。基于我们的性能评估工具，新模型显著优于采用对数高斯考克斯过程的现有方法。我们还获得了初步证据，表明带标记的PCP模型相较于无标记模型能提升UDG探测性能。此外，我们发现了一个潜在的新"暗星系"证据，该星系未被以往方法探测到。