  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.
