Marginal Girsanov Reweighting: Stable Variance Reduction via Neural Ratio Estimation

Abstract: Recovering unbiased properties from biased or perturbed simulations is a central challenge in rare-event sampling. Classical Girsanov Reweighting (GR) offers a principled solution by yielding exact pathwise probability ratios between perturbed and reference processes. However, the variance of GR weights grows rapidly with time, rendering it impractical for long-horizon reweighting. We introduce Marginal Girsanov Reweighting (MGR), which mitigates variance explosion by marginalizing over intermediate paths, producing stable and scalable weights for long-timescale dynamics. Experiments demonstrate that MGR (i) accurately recovers kinetic properties from umbrella-sampling trajectories in molecular dynamics, and (ii) enables efficient Bayesian parameter inference for stochastic differential equations with temporally sparse observations.