Move from emcee to more modern framework

[ipcamit]

@yonatank93 @mjwen

I think we can look towards more feature rich bayesian framework for UQ, specially for physics based models and smaller MLIPs. While emcee is good, I had something like Pyro or PyMC3 in mind. I prefer Pyro, as it is already compatible with ML models.

Problem comes with KIM-API models, which does not have gradient facility. For them I suggest wrapping torch.autorad.functional in a numdiff wrapper, I have tried it and it works. This will ensure one MCMC+VI framework for entire KLIFF.

Cons: emcee used Metropolis sampling, while Pyro uses hamiltonian monte carlo. I think it makes no difference as statistically both sample the posterior the same, but not an expert. What do you think yonathan?

Compromise will be to implement own AIES algorithm (emcee) in Pyro, but that would be my last resort.

What do you guys think? Worth the efforts? We will gain the ability to train any model in full bayesian framework.

[yonatank93]

I think that is definitely a good direction moving forward. I also recognize that emcee is not as popular as PyMC3 and Pyro. Maybe instead of replacing emcee with Pyro, we can add Pyro as an option. Or rather, Pyro would be the default framework with an option to use emcee.

There are 2 reasons why I use emcee instead of the other packages. First, emcee just happened to be the package I learned first (Mark suggested it), so I am more familiar with it. Second, emcee (and ptemcee) support parallel tempering MCMC, which has its own appeal. However, I also understand that if we stick with emcee, it will limit the applicability of MCMC in KLIFF.

So, I support if we want to use Pyro. I just don't have time to learn about it and implemented currently.

[ipcamit]

OK. I will leave the emcee stuff intact. And add a more general MCSampler class in UQ using HMC and Pyro.