## generalised bouncy particle sampler

**M**y PhD student, Wu Changye, just completed a paper on an extension of the bouncy particle sampler, to which he associated me as we had discussed the contents and especially the proofs together, although I did not participate in the redaction of the paper. The bouncy particle sampler belongs to the collection of piecewise deterministic samplers, which also contains the recent zig-zag sampler of Joris Bierkens, Paul Fearnhead, and Gareth Roberts (Warwick). It was introduced by Alexandre Bouchard-Côté, Sebastian Vollmer (Warwick) and Arnaud Doucet, to appear in JASA, and uses one particle that is characterised by the pair (position, velocity), the velocity only changing at random times determined by the target density. The change is also deterministic. Which may lead to a lack of irreducibility in the process and is solved by an extra Poisson process in the original paper. In the generalisation imagined by Changye, the bounce becomes partly random in the direction orthogonal to the gradient. The stationarity results of Bouchard-Côté, Vollmer and Doucet then extend to this setting. As does the ability to subsample and compute faster versions of the likelihood function.

June 19, 2017 at 10:10 am

We, George Deligiannidis, Alex Bouchard-Cote and myself, have recently obtained geometric ergodicity results for the bouncy particle sampler (https://arxiv.org/abs/1705.04579). It’d be interesting to see whether they can be extended to this algorithm.

June 19, 2017 at 11:40 am

Ỳes indeed, I have seen the paper if not yet commented on it! Thanks!