Multilevel Monte Carlo methods in PyMC3

Hi all,

This is my very first time here, I have been using PyMC3 for a while in the context of Uncertainty Quantification and Bayesian Calibration. Thanks a lot for this great tool!

Straight to the point: do you ever have heard about Multilevel Monte Carlo (MLMC) methods proposed by Mike Giles? This is not exactly Hierarchical modeling as we have in PyMC3 docs. Please check it out here. Actually, it is based on Multigrid idea of coarse/fine cycles (for those who appreciate advanced numerical linear algebra arts). It can provide a great performance improvement when you have computationally demanding simulations inside your analysis. For instance, QUESO has this method available.

What do you think about MLMC? Is it worthy to have it in PyMC3 (maybe in PyMC4 in the future)?

I have been using CATMIP (awesome method!), but MLMC would be nice to have too.