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Statistics on fields with index sets of more than one dimension of support and, frequently, an implicit 2-norm. Sometimes they are also time-indexed. Especially, for processes on a continuous index set with continuous state and undirected interaction. Sometimes over fancy manifolds, although often you can get away with plain old euclidean space, unless you if you are doing spatial statistics over the entire planet, which turns out to be curved. Lattice models are frequently considered spatial statistics, but more arbitrary graph structures usually get filed under undirected graphical models/random fields. For spatial point processes I will make a new notebook. Often we mean some kind of Gaussian process regression to handle spatial statistics, although the use of these tool in the ML and spatial literatures is weirdly disjoint. There are many other random fields we might also wish to infer that relate to spatial index sets, and these can be taxonomised as I notice their existence. There are lots of interesting problem with statistics on such fields. Consider the illustrative problem of declustering.
I’m curious about how spatial statistics generalise to high-dimensional fields such as fitness landscapes, loss functions, and embedding of network processes in space…
The spatial statistics name for Gaussian process regression.
Spatial point processes
All recomendations made to me and passed on here are offered unreviewed and unendorsed.
Spatstat is the reference general-purpose spatial data analysis. based on R.
PySAL Python. Library of statistical functions for continuous-state spatial processes.
Passage is also Python. GUI full of statistical analyses.
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