Implement the discrete bouncy particle sampler

[AdrienCorenflos]

Presentation of the new sampler

This is a discretised version of the bouncy particle sampler (see https://github.com/blackjax-devs/blackjax/issues/241), which happens to not require simulating Poisson processes and to have "classical" ergodic properties compared to PDMPs.

It is published at Biometrika: https://academic.oup.com/biomet/article/109/2/335/6151695

How does it compare to other algorithms in blackjax?

Compared to classical MCMC algorithm it does not (necessarily) preserve the detailed balanced condition, and allows for non-diffusive exploration of the state-space (more efficient than random-walk like methods).

Contrarily to standard PDMPs, the implementation is in fact rather easy (beside preconditioning) and is very compatible with BlackJAX.

Where does it fit in blackjax

This would be the first non-reversible algo in BlackJAX and would signal interest in these methods.

Are you willing to open a PR?

Yes, of course :) but it is actually also a rather simple algo that can be implemented by new comers!