We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice since most point pattern data consist of only one pattern. We therefore explore the possibility to condition on the number of points instead when fitting and validating spatial point process models. In a simulation study with different popular spatial point process models, we consider model validation using global envelope tests based on functional summary statistics. We find that conditioning on the number of points will for some functional summary statistics lead to more narrow envelopes and that it can also be useful for correcting for some conservativeness in the tests when testing composite hypothesis. However, for other functional summary statistics, it makes little or no difference to condition on the number of points. When estimating parameters in popular spatial point process models, we conclude that for mathematical and computational reasons it is convenient to assume a distribution for the number of points.
翻译:我们讨论了在模拟空间点模式时直接或间接假设一个点数模式的模式的做法,尽管很少可能在实践中验证这种模式,因为大多数点样数据只有一个模式。因此,我们探讨是否可能在适当和验证空间点进程模型时以点数为条件,而不是在适当和验证空间点进程模型时以点数为条件。在对不同的广受欢迎的空间点进程模型进行模拟研究时,我们考虑使用基于功能摘要统计的全球信封测试来验证模型。我们发现,某些功能摘要统计以点数为条件将会导致更窄的封套,而且对于在测试综合假设时纠正测试时的保守性也是有益的。然而,对于其他功能摘要统计来说,它很少或根本没有区别点数。在估计流行空间点进程模型参数时,我们的结论是,出于数学和计算上的理由,假设点数分布是方便的。