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Creators/Authors contains: "Kleppe, Tore"

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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. ; (, 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