🤖 AI Summary
This study addresses the challenge that observed spatial point patterns are often degraded by missed detections (sparsity) and positional errors (displacement), which can severely bias inference. Focusing on Poisson point processes, the authors propose a unified framework that jointly estimates the underlying intensity function nonparametrically while simultaneously learning a parametric model for both the sparsity mechanism and the displacement scale. Under mild conditions, they rigorously establish model identifiability—a first for enabling joint nonparametric inference of the degradation mechanisms and the true intensity function. Simulations demonstrate that the proposed method substantially outperforms misspecified models that ignore such observational degradations. The approach is successfully applied to real-world data on North Atlantic right whale calls in Cape Cod Bay, showcasing its practical utility.
📝 Abstract
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.