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In this paper we provide performance guarantees for hypocoercivenon-reversible MCMC samplers $X_t$ with invariant measure $\mu^*$ and ourresults apply in particular to the Langevin equation, Hamiltonian Monte-Carlo,and the bouncy particle and zig-zag samplers. Specifically, we establish aconcentration inequality of Bernstein type for ergodic averages $\frac{1}{T}\int_0^T f(X_t)\, dt$. As a consequence we provide performance guarantees: (a)explicit non-asymptotic confidence intervals for $\int f d\mu^*$ when using afinite time ergodic average with given initial condition $\mu$ and (b)uncertainty quantification bounds, expressed in terms of relative entropy rate,on the bias of $\int f d\mu^*$ when using an alternative or approximateprocesses $\widetilde{X}_t$. (Results in (b) generalize recent results(arXiv:1812.05174) from the authors for coercive dynamics.) The concentrationinequality is proved by combining the approach via Feynmann-Kac semigroupsfirst noted by Wu with the hypocoercive estimates of Dolbeault, Mouhot andSchmeiser (arXiv:1005.1495) developed for the Langevin equation and recentlygeneralized to partially deterministic Markov processes by Andrieu et al.(arXiv:1808.08592)

Concentration inequalities and performance guarantees for hypocoercive MCMC samplers