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This technical report is the union of two contributions to the discussion ofthe Read Paper "Riemann manifold Langevin and Hamiltonian Monte Carlo methods"by B. Calderhead and M. Girolami, presented in front of the Royal StatisticalSociety on October 13th 2010 and to appear in the Journal of the RoyalStatistical Society Series B. The first comment establishes a parallel andpossible interactions with Adaptive Monte Carlo methods. The second commentexposes a detailed study of Riemannian Manifold Hamiltonian Monte Carlo (RMHMC)for a weakly identifiable model presenting a strong ridge in its geometry.

Discussion of "Riemann manifold Langevin and Hamiltonian Monte Carlo methods'' by M. Girolami and B. Calderhead