Sticky coupling as a control variate for sensitivity analysis
A standard method to estimate the sensitivity of the invariant measure of a given stochastic dynamics to perturbations by a small forcing is to simulate it up to a time $T$ and time-average over the trajectory a desired observable divided by the magnitude of the forcing, $\eta$. Unfortunately, this method suffers from large finite-time sampling bias and variance in the limit of small forcing—on the order of $(T\eta)^{-1}$ and $(T\eta^2)^{-1}$ respectively. For dynamics given by an SDE with additive noise, we propose a control variate approach using a sticky coupled version of the unperturbed dynamics. We show that when the drift is strongly contractive at infinity, this sticky coupling based estimator reduces the bias and variance by a factor of $\eta^{-1}$ compared to the standard method. Our hypotheses include systems commonly used in molecular dynamics such as overdamped Langevin dynamics with Lennard-Jones interaction potential and quadratic confining potential.
Area: CS36 - Monte Carlo methods and Applications II (Francesca R Crucinio, Alessandra Iacobucci, Andrea Bertazzi)
Keywords: sticky coupling
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