Timeline for Spatial Point Process: Does an inhomogeneous first order intensity function affect the second order dependence?
Current License: CC BY-SA 4.0
8 events
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| Jun 6, 2019 at 13:45 | comment | added | whuber♦ | @Ege Thank you for that analysis. It strikes me that the extreme model you describe is a kind of high-parameter-count, "saturated" model that could be compared to other parsimonious models in standard ways (through AIC, cross-validation, etc), thereby making it possible to develop objective, informed opinions about the nature of the underlying process. | |
| Jun 6, 2019 at 6:52 | comment | added | Ege Rubak | I agree that with reasonable assumptions you can have some luck in using a single point pattern to separate inhomogeneity and "real" clustering (and more easily inhibition) due to interactions between points. However, you can always refer to the degenerate case and say that the underlying process is inhomogeneous Poisson with virtually point masses at the observed points, so in the mathematical sense without further assumptions I guess you cannot really make progress. Of course this is uninteresting from a practical point of view and not a point of view I'm advocating in any way. | |
| Jun 5, 2019 at 11:52 | comment | added | whuber♦ | Whether it's overfitting depends on how detailed you get. But I understood what you meant and responded to it: it's possible, from a single realization, to find evidence that will suggest the nature of clustering. A study of nearest-neighbor distances is an effective way to find such evidence. | |
| Jun 5, 2019 at 1:29 | comment | added | NamelessGods | I guess I was not clear enough on what I meant. I meant if I only have one data set of a point process that I know nothing about, e.g., the clustered point process in your second example. It does seem to me that in this case there is no way I can distinguish first-order inhomogeneity and second-order dependence structure. Since it does seem possible for me to fit a very detailed first order intensity function to describe the process as well as the nearest neighbor gaps. That is of course overfitting. Nevertheless, it seems to prove my point. | |
| Jun 5, 2019 at 1:05 | comment | added | whuber♦ | I disagree with that conclusion, because an analysis of the nearest-neighbor gaps can help distinguish them. I would agree that in many cases it may be difficult to distinguish those phenomena, but it's definitely possible to do so in some cases. | |
| Jun 5, 2019 at 0:50 | comment | added | NamelessGods | Thanks for the reply. This certainly cleared out most of my confusions. However, it also creates another question for me and I want to get this right. From what you said, is it true that if I don't know the data generating process and I only have one realization of the point process, then the first order inhomogeneity and second-order dependence structure are always indistinguishable as mentioned by Ege? | |
| Jun 4, 2019 at 19:50 | vote | accept | NamelessGods | ||
| Jun 4, 2019 at 19:08 | history | answered | whuber♦ | CC BY-SA 4.0 |