Should We Condition on the Number of Points When Modelling Spatial Point Patterns?

We discuss the practice of directly or indirectly assuming a model for number points when modelling spatial point patterns even though it is rarely possible to validate such in because most pattern data consist only one pattern. therefore explore possibility condition on instead fitting and validating process models. In simulation study with different popular models, we consider validation using global envelope tests based functional summary statistics. find that conditioning will some statistics lead more narrow envelopes thus stronger can also be useful correcting conservativeness testing composite hypothesis. However, other statistics, makes little no difference points. When estimating parameters conclude mathematical computational reasons, convenient assume distribution