Spatial point processes are used as models in many different fields ranging from ecology and forestry to cosmology and materials science. In recent years, model validation, and in particular goodness-of-fit testing of a proposed point process model have seen many advances. Most of the proposed tests are based on a functional summary statistic of the observed pattern. In this paper, the empirical powers of many possible goodness-of-fit tests that can be constructed from such a summary statistic are compared in an extensive simulation study. Recently introduced functional summary statistics derived from topological data analysis and new constructions for the test statistic such as the continuous ranked probability score are included in the comparison. We discuss the performance of specific combinations of functional summary statistic and test statistic and their robustness with respect to other tuning parameters. Finally, tests using more than one individual functional summary statistic are also investigated. The results allow us to provide guidelines on how to choose powerful tests in a particular test stetting.

翻译：空间点过程作为模型被广泛应用于从生态学、林学到宇宙学与材料科学等诸多领域。近年来，模型验证，特别是针对所提点过程模型的拟合优度检验取得了诸多进展。大多数现有检验方法基于观测模式的函数型摘要统计量。本文通过大规模模拟研究，比较了基于此类摘要统计量构建的多种拟合优度检验方法的经验功效。研究涵盖了源自拓扑数据分析的最新函数型摘要统计量，以及连续排序概率得分等新型检验统计量构造方法。我们探讨了特定函数型摘要统计量与检验统计量组合的性能表现及其对其他调优参数的稳健性。最后，本文还考察了使用多个独立函数型摘要统计量的检验方法。研究结果为在特定检验场景中选择高效能检验方法提供了指导原则。