Langevin Monte Carlo methods for Bayesian inference

Peter Whalley (ETH Zurich)

Tuesday, May 5th, 2026, 3 p.m - TBC

Abstract: We introduce Langevin Monte Carlo methods for estimating expectations of observables under high-dimensional probability measures. We discuss discretization strategies and Metropolization techniques for removing bias due to discretization error. We also present numerical simulations and theoretical guarantees for these methods, and identify settings in which it may be desirable to forgo Metropolization.This motivates a new unbiased method for estimating Bayesian posterior means. Our approach avoids Metropolis correction by coupling Markov chains at different discretization levels within a multilevel Monte Carlo framework. Theoretical analysis shows that the proposed estimator is unbiased, has finite variance, and satisfies a central limit theorem. We establish similar results using both approximate and stochastic gradients, and show that the computational cost of our method scales independently of the dataset size. Numerical experiments demonstrate that our unbiased algorithm outperforms the “gold-standard” randomized Hamiltonian Monte Carlo.