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Creators/Authors contains: "Bou-Rabee, Nawaf"

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  1. ; ; ; (, The Journal of Chemical Physics)
    Adapting the step size locally in the no-U-turn sampler (NUTS) is challenging because the step-size and path-length tuning parameters are interdependent. The determination of an optimal path length requires a predefined step size, while the ideal step size must account for errors along the selected path. Ensuring reversibility further complicates this tuning problem. In this paper, we present a method for locally adapting the step size in NUTS that is an instance of the Gibbs self-tuning (GIST) framework. Our approach guarantees reversibility with an acceptance probability that depends exclusively on the conditional distribution of the step size. We validate our step-size-adaptive NUTS method on Neal’s funnel density and a high-dimensional normal distribution, demonstrating its effectiveness in challenging scenarios. 
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    Free, publicly-accessible full text available August 28, 2026
  2. ; ; (, Electronic Journal of Probability)
    Hit-and-Run is a coordinate-free Gibbs sampler, yet the quantitative advantages of its coordinate-free property remain largely unexplored beyond empirical studies. In this paper, we prove sharp estimates for the Wasserstein contraction of Hit-and-Run in Gaussian target measures via coupling methods and conclude mixing time bounds. Our results uncover accelerated convergence rates in certain settings. Furthermore, we extend these insights to a coordinate-free variant of the randomized Kaczmarz algorithm, an iterative method for linear systems, and demonstrate analogous convergence rates. These findings offer new insights into the advantages and limitations of coordinate-free methods for both sampling and optimization. 
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    Free, publicly-accessible full text available October 17, 2026
  3. ; (, Mathematics of Computation)
    We introduce 5 / 2 5/2 - and 7 / 2 7/2 -order L 2 L^2 -accurate randomized Runge-Kutta-Nyström methods, tailored for approximating Hamiltonian flows within non-reversible Markov chain Monte Carlo samplers, such as unadjusted Hamiltonian Monte Carlo and unadjusted kinetic Langevin Monte Carlo. We establish quantitative 5 / 2 5/2 -order L 2 L^2 -accuracy upper bounds under gradient and Hessian Lipschitz assumptions on the potential energy function. The numerical experiments demonstrate the superior efficiency of the proposed unadjusted samplers on a variety of well-behaved, high-dimensional target distributions. 
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    Free, publicly-accessible full text available February 4, 2026
  4. ; (, The Annals of Applied Probability)
    Free, publicly-accessible full text available February 1, 2026
  5. ; (, Electronic Journal of Probability)
    We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the ‘high acceptance regime’. The approach uses a localization argument to boost local mixing of the underlying unadjusted kernel to mixing of the adjusted kernel when the acceptance rate is suitably high. As an application, mixing time guarantees are developed for a non-reversible, adjusted Markov chain based on the kinetic Langevin diffusion, where little is currently understood. 
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    Full Text Available 
  6. ; (, Bernoulli)
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  7. ; (, Electronic Journal of Probability)
    We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization step to be sufficiently small, but do not require strong convexity of either the unary or pairwise potential terms present in the mean-field model. To handle high dimensionality, our proof uses a particlewise coupling that is contractive in a complementary particlewise metric. 
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    Full Text Available 
  8. ; (, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques)
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  9. ; (, Stochastics and Partial Differential Equations: Analysis and Computations)
    We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequence, explicit and dimension-free bounds for pHMC applied to high-dimensional distributions arising in transition path sampling and path integral molecular dynamics are given. Global convexity of the underlying potential energies is not required. Our results are based on a two-scale coupling which is contractive in a carefully designed distance. 
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    Full Text Available 
  10. ; ; ; (, The Journal of Chemical Physics)
    null (Ed.)
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