Some connections between importance sampling and enhanced sampling methods in molecular dynamics

In molecular dynamics, enhanced sampling methods enable the collection of better statistics of rare events from a reference or target distribution. We show that a large class of these methods is based on the idea of importance sampling from mathematical statistics. We illustrate this connection by comparing the Hartmann-Schütte method for rare event simulation (J. Stat. Mech. Theor. Exp. 2012, P11004) and the Valsson-Parrinello method of variationally enhanced sampling [Phys. Rev. Lett. 113, 090601 (2014)]. We use this connection in order to discuss how recent results from the Monte Carlo methods literature can guide the development of enhanced sampling methods.