5th October 2018, 3:30 pm – 4:30 pm
Main Maths Building, SM3
I will discuss some recent results on PDMCMC and in particular on the Bouncy Particle Sampler (BPS). In particular I will show that as the dimension of the target grows, at least for targets that factorise or satisfy some other weak dependence assumption, any finite collection of location and momentum coordinates of BPS converge weakly to the corresponding Randomized Hamiltonian Monte Carlo (RHMC). This is essentially a piecewise deterministic version of the well known HMC algorithm and therefore this establishes a close link between BPS and Hamiltonian dynamics. Next, I will go through some methods for obtaining dimension free convergence rates for RHMC and discuss its implications on the computational cost of BPS. This is joint work with D. Paulin, A. Bouchard-Côté and A. Doucet.