6 problems

Let generalized Monte Carlo (GMC) be the discrete-time reflective Hamiltonian Markov chain described in the surrounding construction. An extension to continuous-time dynamics would…

HMC convergence conjecture. Theorem should hold for the HMC algorithm as well. The conjecture proposes that the paper's main non-asymptotic convergence result in total variation ex…

Let $T$ denote the HMC integration time, subject to the time-step restriction discussed in the analysis. Time-step optimality conjecture. For many problems of interest, this restri…

Consider gradient-based Markov chain Monte Carlo methods, including Hamiltonian Monte Carlo (HMC), applied to rough energy landscapes. Generic-gradient-stiffness conjecture. The we…

Let $\pi_{\sigma}$ be a mixture distribution of the form … where $f_{1},\ldots,f_{k}$ are probability densities, $\mu_{1},\ldots,\mu_{k}\geq 0$ are fixed weights satisfying…

Let Algorithm denote the approximate randomized Hamiltonian Monte Carlo algorithm, and let the potential energy function and the reversible, volume-preserving integrator satisfy su…