Goodness-of-fit tests for spatial point processes: A power study

Abstract: 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.