Statistics of spatio-temporal processes



The dynamics of spatial processes evolving in time.

Clearly there are many different problems one might wonder about here. I am thinking in particular of the kind of problem whose discretisation might look like this, as a graphical model.

This is highly stylized - I’ve imagined there is one spatial dimension, but usually there would be two or three. The observed notes are where we have sensors that can measure the state of some parameter of interest \(w\) which evolves in time \(t\). I am wondering what we need to control for to simultaneously learn the parameters of the spatial field \(r_i\), the (possibly emulated) process \(p\) and the state of the unobserved \(w\) nodes.

Intros

Cosma Shalizi’s Data Over Space and Time course.

Tools

geostack

…is a toolkit for high performance geospatial processing, modelling and analysis.

Some highlights of Geostack include:

  • Range of programmable geospatial operations based on OpenCL, including map algebra, distance mapping and rasterisation.
  • Data IO for common geospatial types such as geotiff and shapefiles with no dependencies.
  • Implicit handling geospatial alignment and projections, allowing easier coding of geospatial models.
  • Python bindings for interoperability with GDAL/RasterIO/xarray/NetCDF.
  • Built-in computational solvers including level set and network flow models.

More information and build guides are on our wiki.

Geostack can be installed for Python using conda.

gstat does certain R stats.

References

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