[R-sig-Geo] 3D Point Pattern Summary Statistics

[Rajagopal Vijayaraghavan]

Hi,

I would like some expert guidance with an issue I am having; I hope this is the right place to ask this question. 

I want to test the validity of a non-parametric model to simulate a 3D point pattern. I am using the G-function and a-priori knowledge on restrictions on the pattern (there is an attraction for the points towards an anatomical landmark that I have quantified) as the basis of an energy function I minimize through a form of poisson thinning with the aim of matching the statistical measures that have been observed in the real data. 

I use the F3est, K3est, pcf3Est and G3est functions to generate the envelopes from this non-parametric model to then see if my observed data (that I used to generate the stats for the energy function in the first place) fits into the envelope. 

I find that the K, G and pcf of the observed data fits well within the envelopes of K, G and pcf from the 99 simulated point patterns. However, I find that the F function of the observed is slightly outside the envelope for the F from the simulations. My questions are:

(i) If G, K and pcf (I acknowledge that K and pcf are related) fit into the envelope, then F should, should it not? F(r) is the proportion of the nearest points in the point process that are less than r away from an arbitrary point in the window. The K and G are related to some degree to this aren't they?

(ii) How far out of the envelope is too far? I guess I am asking if the envelope test is a hard black/white kind of rule or does one think of the context and justify how sincerely one must adhere to the envelope test for these different summary statistics?

I would like to note that I have kept the details to a minimum to save time, but I do have these plots and can give further explanation if needed. Thank you for your help in advance.

best wishes

Vijay