## Archive for interacting particle systems

## yet another opportunity in a summer of Briton conferences, free of charge!

Posted in Statistics with tags Bretagne, Brittany, Henri Lebesgue, interacting particle systems, mini-courses, Rennes, simulation, simulation and probability on April 10, 2018 by xi'an## bouncy particle sampler

Posted in pictures, Statistics, Travel, University life with tags curse of dimensionality, Gibbs sampler, Hamiltonian Monte Carlo, interacting particle systems, Monte Carlo Statistical Methods, particle, pinball sampler, Teneriffe on October 30, 2015 by xi'an** 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.

## interacting particle systems as… facebook

Posted in Books, Statistics, University life with tags Bernoulli, David Aldous, Facebook, Galton-Watson process, interacting particle systems, Kingman's coalescent on October 8, 2013 by xi'an**A**mong the many interesting arXived papers this Friday, I first read David Aldous’ “Interacting particle systems as stochastic social dynamics“. Being unfamiliar with those systems (despite having experts in offices down the hall in Paris-Dauphine!), I read this typology of potential models (published in *Bernoulli*) with a keen interest! The paper stemmed from a short course given in 2012 in Warwick and Cornell. I think the links exhibited there with (social) networks should be relevant for statisticians working on networks (!) and dynamic graphical models. Statistics is not mentioned in the paper, except for the (misleading) connection with statistical physics, but there is obviously a huge potential for statistical inference, from parameter estimation to model comparison. (As pointed out by David Aldous, there is usually “no data or evidence linking the model to the asserted real-world phenomena”.) The paper then introduces some basic models like the token, the pandemic and the averaging process, plus the voter model that relates to Kingman’s coalescent. A very nice read opening new vistas for sure (and a source of projects for graduate students most certainly!)