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We discuss the practice of directly or indirectly assuming a model for thenumber of points when modelling spatial point patterns even though it is rarelypossible to validate such a model in practice since most point pattern dataconsist of only one pattern. We therefore explore the possibility to conditionon the number of points instead when fitting and validating spatial pointprocess models. In a simulation study with different popular spatial pointprocess models, we consider model validation using global envelope tests basedon functional summary statistics. We find that conditioning on the number ofpoints will for some functional summary statistics lead to more narrowenvelopes and that it can also be useful for correcting for someconservativeness in the tests when testing composite hypothesis. However, forother functional summary statistics, it makes little or no difference tocondition on the number of points. When estimating parameters in popularspatial point process models, we conclude that for mathematical andcomputational reasons it is convenient to assume a distribution for the numberof points.

Should we condition on the number of points when modelling spatial point patterns?