Add spatial autocorrelation statistics (Moran's I, LISA, Geary's C)

[brendancol]

Motivation

We already have Getis-Ord Gi* via hotspots() and emerging_hotspots(), but Moran's I (global and local/LISA) is the other fundamental spatial statistic that most analysis workflows depend on. Right now users have to leave xarray-spatial to compute these, which breaks the pipeline.

Scope

Statistics:

• Global Moran's I
• Local Moran's I (LISA) with significance testing via random permutation
• Geary's C (global and local)
• Join count statistics for categorical rasters

Spatial weights:

• Queen and rook contiguity derived from the raster grid structure
• Distance-band weights (binary and inverse-distance)

Implementation notes

• Should follow the existing backend dispatch pattern: numpy, cupy, dask+numpy, dask+cupy via ArrayTypeFunctionMapping.
• Local statistics (LISA, local Geary) return xarray DataArrays matching the input grid. Global statistics (Moran's I, Geary's C) return scalar results.
• P-values from permutation testing should be included in the output, either as a second DataArray or as attributes.
• Permutation-based significance is embarrassingly parallel and maps well to both dask chunks and GPU threads.

Related

• hotspots() already computes Gi* z-scores
• emerging_hotspots() does temporal hot spot classification
• PySAL/esda covers this for vector data, but there's nothing raster-native