The purpose of the present article is to compare different phase-space
sampling 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 purely
deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive
Multiple Thermostats (RMT) methods). After recalling
some theoretical convergence properties for
the various methods, we provide some new convergence results
for the Hybrid Monte Carlo scheme, requiring weaker (and easier to
check) conditions than previously known conditions. We then turn to the numerical
efficiency of the sampling schemes for a benchmark model of linear
alkane molecules.
In particular, the numerical
distributions that are generated are compared in a systematic way, on the basis
of some quantitative
convergence indicators.