How to tune sampling algorithms for Bayesian inference from simulations

When inferring parameters from simulation models, combining multiple observations requires aggregating learned score functions—but this composite score doesn't match any true distribution, introducing bias. Annealed Langevin dynamics sidesteps this by treating the composite score as exact and sampling through a sequence of bridging densities. The authors derive Wasserstein error bounds and convert them into explicit tuning rules for step sizes, iteration counts, and annealing levels. In Gaussian settings, they prove one recent method requires fewer total steps than another; empirically, those rules generalize to nonlinear problems, giving practitioners a theoretically grounded starting point instead of ad-hoc hyperparameter choices.