Using Bayes formula to estimate rates of rare events in transition path sampling simulations

TL;DR

This paper introduces a Bayesian approach to improve the estimation of rare event rates in transition path sampling, enabling more efficient and accurate calculations in molecular systems.

Contribution

The authors develop a Bayesian method that constructs biased samples with more reactive trajectories and estimates transition rates directly, addressing convergence issues in traditional sampling techniques.

Findings

Bayesian approach enhances sampling efficiency.

Method reduces convergence problems in rate estimation.

Improves accuracy of rare event rate calculations.

Abstract

Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in which these rare trajectories have become frequent. Then, a multistate reweighting scheme is implemented to postprocess data collected from the staged simulations. Herein, we show how Bayes formula allows to directly construct a biased sample containing an enhanced fraction of reactive trajectories and to concomitantly estimate the transition rate from this sample. The approach can remediate the convergence issues encountered in free energy perturbation or umbrella sampling simulations when the transformed distribution insufficiently overlaps with the reference distribution.