DeepAI AI Chat
Log In Sign Up

Martingale product estimators for sensitivity analysis in computational statistical physics

by   Petr Plechac, et al.

We introduce a new class of estimators for the linear response of steady states of stochastic dynamics. We generalize the likelihood ratio approach and formulate the linear response as a product of two martingales, hence the name "martingale product estimators". We present a systematic derivation of the martingale product estimator, and show how to construct such estimator so its bias is consistent with the weak order of the numerical scheme that approximates the underlying stochastic differential equation. Motivated by the estimation of transport properties in molecular systems, we present a rigorous numerical analysis of the bias and variance for these new estimators in the case of Langevin dynamics. We prove that the variance is uniformly bounded in time and derive a specific form of the estimator for second-order splitting schemes for Langevin dynamics. For comparison, we also study the bias and variance of a Green-Kubo estimator, motivated, in part, by its variance growing linearly in time. Presented analysis shows that the new martingale product estimators, having uniformly bounded variance in time, offer a competitive alternative to the traditional Green-Kubo estimator. We compare on illustrative numerical tests the new estimators with results obtained by the Green-Kubo method.


page 1

page 2

page 3

page 4


On Generalized Schürmann Entropy Estimators

We present a new class of estimators of Shannon entropy for severely und...

Convergence of the likelihood ratio method for linear response of non-equilibrium stationary states

We consider numerical schemes for computing the linear response of stead...

Stochastic Zeroth Order Gradient and Hessian Estimators: Variance Reduction and Refined Bias Bounds

We study stochastic zeroth order gradient and Hessian estimators for rea...

Non-reversible sampling schemes on submanifolds

Calculating averages with respect to probability measures on submanifold...

Error estimates and variance reduction for nonequilibrium stochastic dynamics

Equilibrium properties in statistical physics are obtained by computing ...

Accelerated Jarzynski Estimator with Deterministic Virtual Trajectories

The Jarzynski estimator is a powerful tool that uses nonequilibrium stat...

Unifying Design-based Inference: A New Variance Estimation Principle

This paper presents two novel classes of variance estimators with superi...