Robin Ryder - Coupling MCMC algorithms on submanifolds

Markov Chain Monte Carlo (MCMC) is a versatile tool to sample from intractable distributions and construct consistent approximations of integrals, but it is difficult to measure the convergence speed of MCMC on complex spaces. Jacob et al. (2020) propose a new technique to guarantee the quality of the approximation after finitely many iterations, based on coupling pairs of MCMC algorithms.
We develop MCMC couplings for the special case of a distribution taking values on a submanifold of an ambient space. We demonstrate the efficiency of this approach, and show how to extend these ideas to generic sampling problems.
Work in progress, joint with Elena Bortolato (Padova) and Pierre Jacob (ESSEC).