## bouncy particle sampler

** A**lexandre Bouchard-Coté, Sebastian Vollmer and Arnaud Doucet just arXived a paper with the above title, which reminded me of a proposal Kerrie Mengersen and I made at Valencia 7, in Tenerife, the [short-lived!] pinball sampler. This sampler was a particle (MCMC) sampler where we used the location of the other particles to avoid their neighbourhood, by bouncing away from them according to a delayed rejection principle, with an overall Gibbs justification since the resulting target was the product of copies of the target distribution. The difficulty in implementing the (neat!) idea was in figuring out the amount of bouncing or, in more physical terms, the energy allocated to the move.

In the current paper, inspired from an earlier paper in physics, the Markov chain (or single particle) evolves by linear moves, changing directions according to a Poisson process, with intensity and direction depending on the target distribution. A local version takes advantage of a decomposition of the target into a product of terms involving only some components of the whole parameter to be simulated. And hence allowing for moves in subspaces. An extension proposed by the authors is to bounce along the Hamiltonian isoclines. The method is demonstrably ergodic and irreducible. In practice, I wonder at the level of calibration or preliminary testing required to facilitate the exploration of the parameter space, particularly in the local version that seems to multiply items to be calibrated.

October 31, 2015 at 5:21 pm

Thank you for your comments Christian.

Regarding your question on how much calibration is needed, so far our experience with the sampler has been positive in this regard. A refreshment rate of 0.5–1 seems a fairly robust default choice for a wide range of problems/dimensionality (see Fig 2 left, and Fig 9 left for examples). The local version of the algorithm does not introduce extra tuning parameters per se, although it does introduce the possibility of doing local refreshment, which worked better in our simulations (Section 5.3).

We will look into the connection with the pinball sampler, thank you for pointing it out. Interestingly, the paper by Peters and de With that inspired this work was itself motivated by an application where several ‘particles’ interact—in their case, the ‘particles’ are more literal and model neutral atoms or molecules repulsed by Lennard-Jones potentials.

Best,

Alex