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 woudl 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 process \(p\) and the state of the unobserved \(w\) nodes.




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