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In particular, how do you assess whether a particular spatial process, based on one observation of the process in question, belongs to a particular family of stochastic spatial processes.

For instance, let's imagine that you observe star distributions. You build a theoretical model of cluster processes to model star distributions: for instance, a Poisson process to model centroids of star clusters, and at each point (centroid) of the parent process, a second process consisting of points (stars) randomly distributed in a circle of radius R around the star cluster's centroid (R being itself a random variable).

Which metric would you use to assess whether your observation (star distribution) fits with the theoretical model? Which simple functional uniquely identifies a specific spatial process? I'm looking at very simple metrics such as star counts within some regions, and distances between stars (mean, standard deviation, distribution).

For instance, let's imagine that you observe star distributions. You build a theoretical model of cluster processes to model star distributions: for instance, a Poisson process to model centroids of star clusters, and at each point (centroid) of the parent process, a second process consisting of points (stars) randomly distributed in a circle of radius R around the star cluster's centroid (R being itself a random variable).

Which metric would you use to assess whether your observation (star distribution) fits with the theoretical model? Which simple functional uniquely identifies a specific spatial process? I'm looking at very simple metrics such as star counts within some regions, and distances between stars (mean, standard deviation, distribution).

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