Multiple projection MCMC algorithms on submanifolds

Abstract

We propose new Markov Chain Monte Carlo 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.

References in corpus (2)

• Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
• Non-reversible sampling schemes on submanifolds

Cited by in corpus (5)

• Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
• Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks
• Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents
• Constraint-Based Regularization of Neural Networks
• Non-reversible sampling schemes on submanifolds