Add Vecchia approximation

[samanklesaria]

I thought I might add the Vecchia approximation, as described in https://arxiv.org/pdf/2102.13299.pdf.

[willtebbutt]

Thanks for opening this @samanklesaria . Will be good to have!

Does the Vecchia approximation provide an approximation to the log marginal likelihood? Would be great to have that available if possible.

[willtebbutt]

@samanklesaria please do let me know when this is ready for another review.

[samanklesaria]

@willtebbutt all set for another review! I don't know why all the CI jobs are failing, but it seems to be unrelated to the code here.

[willtebbutt]

Thanks for improving the PR. I've made a few cosmetic remarks, but I think we're nearly ready to go now.

[willtebbutt]

Ah, sorry, you'll need to import log2\pi from IrrationalConstants.jl -- that's causing test failures in your tests at the minute.

[samanklesaria]

My gradient tests are failing now- investigating it.

[samanklesaria]

Everything seems to be working! Thanks for the suggestions.

[willtebbutt]

Wonderful -- just a couple of formatting suggestions to fix, then we can merge.

[samanklesaria]

Are the changes from JuliaFormatter enough, or should I fix other formatting issues as well?

[willtebbutt]

I'm going to merge as-is if you're happy @samanklesaria -- the AD issues will need to be addressed in another PR.

[samanklesaria]

Sounds good! I can't seem to reproduce the AD issues. Might have been a quirk with an inconsistent Revise state.

[willtebbutt]

Ooo before I merge, could you please bump the version number in the Project.toml to 0.4.6 so that I can tag a release?

[willtebbutt]

Thanks for bumping the version. I'm going to merge + tag despite the test failures, because AD problems need to be addressed elsewhere.

[willtebbutt]

Thanks for the contribution @samanklesaria