  The Self-Healing Umbrella Sampling (SHUS) algorithm is an adaptive biasing
algorithm which has been proposed to efficiently sample a multimodal
probability measure. We show that this method can be seen as a variant of the
well-known Wang-Landau algorithm. Adapting results on the convergence of the
Wang-Landau algorithm, we prove the convergence of the SHUS algorithm. We also
compare the two methods in terms of efficiency. We finally propose a
modification of the SHUS algorithm in order to increase its efficiency, and
exhibit some similarities of SHUS with the well-tempered metadynamics method.
