bouncy particle sampler

 Alexandre 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.

València 9 snapshot [2]

During the poster session of Thursday night, between talking with old friends and keeping my bedtime in sight, I only had the opportunity to see less than one fourth of the posters! This is unfortunate as there were [too] many good things there. In particular, I talked with Mark Girolami about his Hamiltonian version of the MCMC algorithm. (This paper is most likely going to be a discussion paper at the Royal Statistical Society, so I will discuss it later!) I also saw a poster on ABC using a pseudo-likelihood to resort to the pseudo-MLE as a summary statistic. Leaving early allowed me to go running in Friday morning and enjoy a beautiful sunrise.

The computational session of Friday morning was (of course!) quite interesting and I discovered the TPA algorithm of Mark Huber that somehow looks like an “exact” nested sampling. (Is this getting into a Valencia tradition?!) The convergence results were surprising but, as Gareth Roberts pointed out, the applicability of the method is limited to cases where slice sampling also applies… Hedie Lopes gave a very enjoyable rendering of his particle learning paper, acknowledging more clearly the dependence of the convergence speed on the number of observations. Nick Polson gave a talk about sparsity and Lasso that related with James-Stein estimators, bringing back memories of my early research, but I am not convinced that minimaxity imperatives and sparsity requirements are that compatible… One of the last talks of the day was by Chris Holmes about harnessing the immense power of graphic cards or even playstations into parallel processing and this was a wonderful prospect, even though the programming that it involves is not innocuous. (This also reminded me of Peter Green’s feat in using the power of laser-printers at a [not-that-remote] time they were the most powerful machine in his department!)

JSM 2009 impressions [day 4]

A very full day today, where I wish I could have been ubiquitous…! I first attended the particle learning session, and thus missed both Gabor Lugosi’s Medallion lecture and the memorial session for David Friedman. The particle learning session has several interesting talks, among which Raquel Prado’s with informed priors about roots in an AR model and Christian Macaro‘s on an innovative construction of mixtures of AR chains as volatilities to overcome the difficulty in handling long memory processes. I then chaired the session organised by Julien Cornebise on population Monte Carlo, a quite exciting and well-attended session, where I found the results of Mark Huber on the product estimator to offer some strong potential to study nested sampling. This means I missed Charlie Geyer’s talk, among others. The afternoon session was where I talked, along with Jun Liu and Simon Tavaré, who both gave talks full of exciting directions in connection with genomics. The planning was so horrendous that both Gareth Roberts and Judea Pearl were giving special invited lectures at the time, not to mention four Bayesian sessions in parallel… The day ended with the COPSS awards, among which The Florence Nightingale David Award was awarded to Nancy Reid for her role model in the profession, a well-deserved recognition indeed!