Statistics on fields with more than one dimension of support and, frequently,
an implicit 2-norm. This might not look like the independent data points
you’re used to, since you can’t have independence in quite the same way you’re
used too, not for smoothly varying processes that have their constraints along
multiple axes.
I’m interested in these because spatial processes seem likely to occur in the
distribution of agent behaviour on a landscape. I’m also curious about how
spatial statistics generalise to high-dimensional fields such as fitness
landscapes, and embedding of network processes in space.
Geographic Information Systems are repositories of of spatial statistical
tools with a GUI.
The classic measure of spatial correlation seems to be Moran’s I, or the
nearly-equivalent Geary’s C. Interestingly, these assume no metric whatever,
but accept neighbour weighting matrices as their inputs. As such, they work on
graphs, in arbitrary dimensional spaces all other clustering arrangements that
a fevered imagination can produce. They do assume classic linear correlation,
though, which seems unlikely to be a feature of any data I have.
I am immersing myself in:
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