On the relation between projections of the reweighted path ensemble

We derive several distribution functions for the recently introduced reweighted path ensemble [Rogal et al. in J. Chem. Phys. 133:174109, 2010]: the configurational and path densities, the reactive current, and the generalized committors for the different path types. We relate these distributions to the free energy and to the expressions for the rate constant in the transition state theory, the reactive flux method, the transition path (interface) sampling framework, and the Bayesian path statistics. In addition, we compute the transmission coefficient (distribution) from the reweighted path ensemble. Finally, we derive the path sampling shooting point distributions. For a simple two dimensional Langevin model we illustrate how these novel distributions can be used as analysis tools in rare event simulations.