Markov chain Monte Carlo algorithms are used to simulate from complex statistical
distributions by way of a local exploration of these distributions. This local feature avoids …

This paper surveys in detail the relations between numerical integration and the Hamiltonian
(or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in …

We introduce a new probabilistic approach to quantify convergence to equilibrium for
(kinetic) Langevin processes. In contrast to previous analytic approaches that focus on the …

Based on a new coupling approach, we prove that the transition step of the Hamiltonian
Monte Carlo algorithm is contractive wrt a carefully designed Kantorovich (L ¹ Wasserstein) …

Supplement to “On the geometric ergodicity of Hamiltonian Monte Carlo”. We provide
additional examples of π-irreducibility, with supporting plots, as well as elaborating on the …

We obtain several quantitative bounds on the mixing properties of an “ideal” Hamiltonian
Monte Carlo (HMC) Markov chain for a strongly log-concave target distribution π on R d. Our …

We propose a new concept of lifts of reversible diffusion processes and show that various
well-known non-reversible Markov processes arising in applications are lifts in this sense of …

In this manuscript we study the properties of a family of a second-order differential equations
with damping, its discretizations, and their connections with accelerated optimization …

In a 1970 Biometrika paper, WK Hastings developed a broad class of Markov chain
algorithms for sampling from probability distributions that are difficult to sample from directly …

This paper discusses the irreducibility and geometric ergodicity of the Hamiltonian Monte
Carlo (HMC) algorithm. We consider cases where the number of steps of the symplectic …