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The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants.
Hybrid Monte Carlo
S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth · 1987
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The acceptance probability in the hybrid Monte Carlo method
S. Gupta, A. Irbäc, F. Karsch, and B. Petersson · 1990
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A generalized guided Monte Carlo algorithm
A. M. Horowitz · 1991
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Probabilistic inference using Markov chain Monte Carlo methods
R. M. Neal · 1993
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Scaling limits for the transient phase of local Metropolis–Hastings algorithms
O. F. Christensen, G. O. Roberts, and J. S. Rosenthal · 2005
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Theoretical and numerical comparison of some sampling methods for molecular dynamics
E. Cances, F. Legoll, and G. Stoltz · 2007
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Splitting and composition methods in the numerical integration of differential equations
S. Blanes, F. Casas, and A. Murua · 2008
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Hybrid Monte Carlo on Hilbert spaces
A. Beskos, F. J. Pinski, J. M. Sanz-Serna, and A. M. Stuart · 2011
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Riemann manifold Langevin and Hamiltonian Monte Carlo methods
M. Girolami and B. Calderhead · 2011
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MCMC using Hamiltonian dynamics
R. M. Neal · 2011
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Bayesian learning for neural networks , volume 118
R. M. Neal · 2012
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Computationally efficient molecular dynamics integrators with improved sampling accuracy
C. Predescu, R. A. Lippert, M. P. Eastwood, D. Ierardi, H. Xu, M. Ø. Jensen, K. J. Bowers, J. Gullingsrud, C. A. Rendleman, R. O. Dror, et al · 2012
Cited alongside, same era.
Optimal tuning of the hybrid Monte Carlo algorithm
A. Beskos, N. Pillai, G. O. Roberts, J. M. Sanz-Serna, and A. M. Stuart · 2013
Cited alongside, same era.
Numerical integrators for the hybrid Monte Carlo method
S. Blanes, F. Casas, and J. M. Sanz-Serna · 2014
Cited alongside, same era.
Stochastic gradient Hamiltonian Monte Carlo
T. Chen, E. Fox, and C. Guestrin · 2014
Cited alongside, same era.
Compressible generalized hybrid Monte Carlo
Y. Fang, J. M. Sanz-Serna, and R. D. Skeel · 2014
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Adaptive multi-stage integrators for optimal energy conservation in molecular simulations
M. Fernández-Pendás, E. Akhmatskaya, and J .M. Sanz-Serna · 2016
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Adaptive splitting integrators for enhancing sampling efficiency of modified Hamiltonian Monte Carlo methods in molecular simulation
E. Akhmatskaya, M. Fernández-Pendás, T. Radivojević, and J. M. Sanz-Serna · 2017
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Randomized Hamiltonian Monte Carlo
N. Bou-Rabee and J. M. Sanz-Serna · 2017
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Palindromic 3-stage splitting integrators, a roadmap
C. M. Campos and J. M. Sanz-Serna · 2017
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Geometric integrators and the Hamiltonian Monte Carlo method
N. Bou-Rabee and J. M. Sanz-Serna · 2018
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Does Hamiltonian Monte Carlo mix faster than a random walk on multimodal densities?
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The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo
M. D. Hoffman and A. Gelman · 2014
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Markov Chain Monte Carlo and Numerical Differential Equations
J. M. Sanz-Serna · 2014
Cited alongside, same era.
Extra chance generalized hybrid Monte Carlo
C. M. Campos and J .M. Sanz-Serna · 2015
Cited alongside, same era.
A Concise Introduction to Geometric Numerical Integration
S. Blanes and F. Casas · 2016
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O. Mangoubi, N. S. Pillai, and A. Smith · 2018
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Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
T. Radivojević, M. Fernández-Pendás, J. M. Sanz-Serna, and E. Akhmatskaya · 2018
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Numerical Hamiltonian Problems
J. M. Sanz-Serna and M. P. Calvo · 2018
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On the geometric ergodicity of Hamiltonian Monte Carlo
S. Livingstone, M. Betancourt, S. Byrne, and M. Girolami · 2019
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Modified Hamiltonian Monte Carlo for Bayesian Inference
T. Radivojević and E. Akhmatskaya · 2019
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