Package scope, interface, composability, etc.

[ElOceanografo]

Opening big-picture issue to discuss what this package should be. My current selfish reason for making it is to be able to construct sparse Distributions.MvNormalCanon distributions I can use in spatial statistical models (in Turing etc.). My ideal long-term vision/wish list for it looks something like:

• A unified mesh interface is worked out (https://github.com/JuliaGeometry/Meshes.jl), so users can define their model mesh however they want and this package will generate a precision matrix for it.
• Current sparse-matrix autodiff issues get figured out, so these precision matrices can be plugged into Turing models and the like.
• Implement a higher level of abstraction so users can easily implement, efficient Markov random spatial fields. Maybe following the interface in AbstractGPs? Except ideally not just Gaussian...
• Specialized, efficient methods for inference and model-fitting (Laplace approximation etc.) are developed.

I guess the biggest question for this repo is whether to keep it focused as a backend implementation of the SPDE method for setting up precision matrices, or to make it more of a complete package for Markov Matern spatial fields (i.e. including more abstract objects and methods for simulation and inference). Relates to the naming discussion in #1.

[jkbest2]

I think the heart of the package is mesh in, precision matrix out.

• The mesh interface will be key. once we have a well-defined mesh interface, extending to one dimension (a mesh is just a Range), non-planar surfaces like spheres, and (probably) three dimensions will mostly just happen.
• Where appropriate, we should register any AD rules, probably in ChainRulesCore.jl.
• I'd be tempted to split out estimation into a separate package, but simulation seems reasonable, where we don't get it from Distributions.jl.
• I'd like to be able to extend this to include anisotropy, nonstationarity, and using other SPDE solutions as the driving noise, but those would happen after we get a solid spatial setup.

[ElOceanografo]

After some more thought, I think I agree that keeping it focused on mesh --> precision matrix is probably the right way to go for now.