Dimension reduction in physical and data sciences

Performance guarantees for hypo-coercive MCMC samplers

Luc Rey-Bellet

University of Massachusetts, Amherst
[SLIDES]

We prove concentration inequalities for several recent and popular non reversible MCMC samplers, for example the bouncy sampler or (a version of) Hamiltonian Monte-Carlo as well for the Langevin equation. We use this result to build rigorous confidence intervals for finite time sampling as well for building UQ ( or robustness) bounds for steady state expectation to control model form uncertainty. This is a joint work with Jeremiah Birell (UMass) and is based on previous joint work with Paul Dupuis (Brown) and Markos Katsoulakis (UMass).