Dynamical computation of the density of states and Bayes factors using nonequilibrium importance sampling

TL;DR

This paper introduces a novel nonequilibrium importance sampling method that provides unbiased estimates with lower variance for computing densities of states and Bayes factors, applicable to high-dimensional systems and Bayesian model comparison.

Contribution

The authors develop a generic importance sampling technique leveraging nonequilibrium trajectories, offering unbiased estimators with reduced variance and applicability to complex systems.

Findings

Efficient density of states computation scales favorably with dimensionality.

Method accurately computes phase diagrams from single trajectories.

Robust application demonstrated in Bayesian model comparison.

Abstract

Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories, and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with provably lower variance than directly estimating the average of an observable. We also establish a direct relation between a dynamical quantity, the dissipation, and the volume of phase space, from which we can compute quantities such as the density of states and Bayes factors. We illustrate the properties of estimators relying on this sampling technique in the context of density of state calculations, showing that it scales favorable with dimensionality -- in particular, we show that it can be used to compute the phase diagram of the mean-field Ising model from a single nonequilibrium trajectory. We also demonstrate the robustness and efficiency of the approach with an application to a Bayesian model comparison problem of the type encountered in astrophysics and machine learning.