Presentation of the new sampler

Pathfinder is already implemented in blackjax. However, if I understand correctly, this implementation is a single-path (algorithm 1 in the paper) pathfinder run. I propose algorithm2, multiple-path pathfinder to approximate complex posterior faster.

If we have a multiple-path pathfinder, it can approximate a more complex posterior better. If we follow algorithm2, we can run one-path pathfinder algorithm multiple times with different initializations in parallel using jax vmap and then apply Arviz's Pareto smoothed importance sampling.

Julia currently has multiple-path pathfinder implementation (https://github.com/mlcolab/Pathfinder.jl/blob/52fef889ec6b579e35d251c0fc5b74628214b98f/src/multipath.jl#L68-L117) so a good reference.

How does it compare to other algorithms in blackjax?

In a high dimensional, multimodal posterior, I can't think of a better algorithm than multiple-pathfinder.

Where does it fit in blackjax

It's an extension of current pathfinder.

Are you willing to open a PR?

Yes or is it already under development?