Support for nautilus sampler

[johannesulf]

I've developed a new Bayesian sampler called nautilus. It's based on combining importance nested sampling with deep learning. This new sampler has been verified to give accurate results on various problems, including exoplanet fitting, as described in the paper on arXiv. I tested nautilus against UltraNest and dynesty as well as other samplers. Out of the box, it needs substantially fewer likelihood evaluations than dynesty and UltraNest. Additionally, it produces very accurate results. Furthermore, evidence estimates produced by nautilus are a factor of ~30 more precise (d log Z ~ 0.01) than that of nested samplers like dynesty and UltraNest.

If there's interest, I'd be happy to help implement nautilus alongside dynesty and UltraNest.

[nespinoza]

Hi @johannesulf,

Thanks for this suggestion and very sorry for the delay --- yes, we would be interested! Feel free to create a branch from dev and implement this. Let us know if you need any help with this!

N.