We show that sampling with a biased Metropolis scheme is essentially equivalent to using the heatbath algorithm. However, the biased Metropolis method can also be applied when an efficient heatbath algorithm does not exist. This is first illustrated with an example from high energy physics (lattice gauge theory simulations). We then illustrate the Rugged Metropolis method, which is based on a similar biased updating scheme, but aims at very different applications. The goal of such applications is to locate the most likely configurations in a rugged free energy landscape, which is most relevant for simulations of biomolecules.
Keywords: Biophysics; Higher energy physics; Markov chain Monte Carlo.