Multiple projection Markov chain Monte Carlo algorithms on submanifolds
Tony Lelièvre, Gabriel Stoltz, Zhang Wei · IMA Journal of Numerical Analysis · 2022
Abstract We propose new Markov chain Monte Carlo (MCMC) algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples.