Locally stationary GPs

[seabbs]

Extend the current GP functionality to be locally stationary by using a patch based approach of stationary Gps with the GP parameters being related with hierarchical distributions. The main issue with this approach is what to do at the boundary between patches. In the first instance I think it makes sense do nothing and see how it goes but if/when that fails I think extending patches to overlap and using a sigmoid or similar to transition from one patch to another might be a good way to go.

As a feature this would support better fitting to retrospective data when the lengthscale has changed over time. It might also be a useful forecasting model in some formulations if you tweak the hierarchical priors to have long lengthscales (as this makes the prior model for future patches that they have long lenghtscales (i.e slower change over time with less variance).

[seabbs]

I plan to work on this in the next few months