Spatial point processes are a valuable tool for probabilistic modeling to explain location data. However, the data themselves are often observed imperfectly. In order to perform accurate inference, one must account for these imperfections, which we refer to as degradation. We consider two forms of degradation for spatial Poisson processes: thinning and displacement. First, we provide some theoretical results on model identifiability, showing that, under weak conditions, one can jointly learn the scale of the displacement, a parametric form of thinning, and a nonparametric intensity function. The ability to learn all of these components and the resulting improvements for inference compared to the conceptual non-degraded but misspecified model are shown empirically via simulation study. Finally, we apply this approach to North Atlantic right whale call data from Cape Cod Bay.

翻译：空间点过程是用于概率建模以解释位置数据的重要工具。然而，数据本身往往被观测得不完全。为了进行精确推断，必须考虑这些不完全性，我们将其称为退化。我们针对空间泊松过程考虑了两种退化形式：稀疏化和位移。首先，我们提供了一些关于模型可识别性的理论结果，表明在弱条件下，可以同时学习位移的尺度、稀疏化的参数形式以及非参数强度函数。通过模拟研究，我们从经验上展示了学习所有这些成分的能力，以及与概念上未退化但错误设定的模型相比，在推断方面的改进。最后，我们将此方法应用于来自科德角湾的北大西洋露脊鲸叫声数据。