The purpose of the present article is to compare different phase-spacesampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling),stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purelydeterministic methods (Nosé-Hoover chains, Nosé-Poincaré and RecursiveMultiple Thermostats (RMT) methods). After recalling some theoretical convergence properties forthe various methods, we provide some new convergence resultsfor the Hybrid Monte Carlo scheme, requiring weaker (and easier tocheck) conditions than previously known conditions. We then turn to the numericalefficiency of the sampling schemes for a benchmark model of linearalkane molecules. In particular, the numerical distributions that are generated are compared in a systematic way, on the basisof some quantitative convergence indicators.
