Envelope tests for spatial point patterns with and without simulation

• DOI: 10.1002/ecs2.1365
• Publication Date: 2016-07-07T17:45:39Z
• Authors: Thorsten Wiegand; Pavel Grabarnik; Dietrich Stoyan
• Keywords: Envelope (radar); Null (SQL); Goodness of fit; Independence

Abstract Model testing is a central step of spatial point pattern analysis, which allows ecologists to judge if their data agree with ecological hypotheses. We present simple and elegant solution challenging problem: the construction goodness‐of‐fit envelope test prescribed significance level α . Our new Analytical Global Envelope ( AGE ) not restricted narrow frame complete randomness its envelopes can be determined by mathematical calculations. This us investigate influence key settings on width strip. To circumvent some assumptions simulation‐free we corresponding Simulation‐Based SBGE test. The strip encircles range summary function such as pair correlation under null model, it has desired property that hypothesis rejected empirical wanders outside envelopes. applied mild conditions values functions model are (approximately) normally distributed independent for different distance bins r j requires only independence assumption. scales broad processes 1/ n , where number points. casts doubt about attempts low (say <100). operate wider strips than classical “pointwise” Therefore, pointwise considered too liberal. Furthermore, show / increases approximately ln( b ), bins. For example, = 20 more 50% study opens up avenues problem in statistics tests widely ecology improve practice testing.