Would appreciate help with the following question which aims to comparing
irregular distributions in 2-dimensional space.
Assume a square grid, dimension n x n (where is on the order of 100), where a
reference distribution is generated by non-random placement of N objects in
this grid (where N is large, on the order of 10^5). The distribution is
"smooth", in that contiguous elements on the grid contain similar number of
objects, generating broad peaks an valleys, but cannot be fitted by any
particular function.
Given subsequent sets of smaller numbers of objects placed onto the same grid,
how could one estimate a probability that this test distribution differs from
the reference distribution (the null hypothesis being that the test set is
simply a small random sample of the reference distribution)? This while
allowing spatial "wobble" in the system, such that peaks in neighboring squares
of the grid are not considered very different.
Apologies if the question is trivial, makes no sense, or is clumsily formulated.
Thanks
Christophe Benoist
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