Abstract: The Hamiltonian Monte Carlo and Langevin processes are kinetic (position/velocity) Markov processes used to sampled target distributions in MCMC methods. In fact, once discretized in time, from a numerical point of view they can be seen as the same algorithm with a different choice of parameters, which makes them amenable to comparison one with the other, in particular in terms of convergence speed toward equilibrium. We will see some results in this direction, focusing on the case of log-concave target distributions, with an exhaustive explicit analysis of the Gaussian case.
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