Goodness-of-fit tests for spatial point processes: A review

Abstract: In this review, the state-of-the-art for goodness-of-fit testing for spatial point processes is summarized. Test statistics based on classical functional summary statistics and recent contributions from topological data analysis are considered. Different approaches to derive test statistics from functional summary statistics are categorized in a unifying notation. We discuss additional aspects such as the graphical representation in terms of global envelopes and the selection of the parameters in the individual tests.