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The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities.
Condition numbers and equilibration of matrices
A van der Sluis · 1969
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Replica Monte Carlo simulation of spin glasses
R H Swendsen and J S Wang · 1986
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Hybrid Monte Carlo
Simon Duane, A D Kennedy, Brian J Pendleton, and Duncan Roweth · 1987
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Matrix Analysis
Roger A Horn, Roger A Horn, and Charles R Johnson · 1990
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Methodologies in spectral analysis of large dimensional random matrices, a review
Zhidong Bai · 1999
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Adaptive estimation of a quadratic functional by model selection
B Laurent and P Massart · 2000
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Annealed importance sampling
Radford M Neal · 2001
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Replica-exchange Monte Carlo method for the isobaric–isothermal ensemble
Tsuneyasu Okabe, Masaaki Kawata, Yuko Okamoto, and Masuhiro Mikami · 2001
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On the acceptance probability of replica-exchange Monte Carlo trials
David A Kofke · 2002
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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
Ernst Hairer, Christian Lubich, and Gerhard Wanner · 2006
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A tutorial on adaptive MCMC
Christophe Andrieu and Johannes Thoms · 2008
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Limiting spectral distribution of XX’ matrices
Arup Bose, Sreela Gangopadhyay, and Arnab Sen · 2010
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MCMC using Hamiltonian dynamics
Radford Neal · 2011
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Hybrid Monte Carlo on Hilbert spaces
Alexandros Beskos, Frank J Pinski, Jesus-Maria Sanz-Serna, and Andrew M Stuart · 2011
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A Short History of Markov Chain Monte Carlo: Subjective Recollections from Incomplete Data
Christian Robert and George Casella · 2011
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Riemann manifold Langevin and Hamiltonian Monte Carlo methods
Mark Girolami and Ben Calderhead · 2011
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Concentration of the information in data with log-concave distributions
Sergey Bobkov and Mokshay Madiman · 2011
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Optimal tuning of the hybrid Monte Carlo algorithm
Alexandros Beskos, Natesh Pillai, Gareth Roberts, Jesus-Maria Sanz-Serna, and Andrew Stuart · 2013
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Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo
T Bui-Thanh and M Girolami · 2014
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Optimizing The Integrator Step Size for Hamiltonian Monte Carlo
Michael Betancourt, Simon Byrne, and Mark Girolami · 2014
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The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
Joshua V Dillon, Ian Langmore, Dustin Tran, Eugene Brevdo, Srinivas Vasudevan, Dave Moore, Brian Patton, Alex Alemi, Matt Hoffman, and Rif A Saurous · 2017
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Probabilistic Magnetotelluric Inversion with Adaptive Regularisation Using the No-U-Turns Sampler
Dennis Conway, Janelle Simpson, Yohannes Didana, Joseph Rugari, and Graham Heinson · 2018
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Inverse problems: From regularization to Bayesian inference
D Calvetti and E Somersalo · 2018
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Does Hamiltonian Monte Carlo mix faster than a random walk on multimodal densities?
Oren Mangoubi, Natesh S Pillai, and Aaron Smith · 2018
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Hamiltonian Monte Carlo solution of tomographic inverse problems
Andreas Fichtner, Andrea Zunino, and Lars Gebraad · 2019
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Matthew D Hoffman · 2014
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TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems
Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dandelion Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng · 2015
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Hamiltonian Monte Carlo and Borrowing Strength in Hierarchical Inverse Problems
Nagel Joseph B. and Sudret Bruno · 2016
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Deep Learning
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Probabilistic programming in Python using PyMC3
John Salvatier, Thomas V Wiecki, and Christopher Fonnesbeck · 2016
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On the Geometric Ergodicity of Hamiltonian Monte Carlo
Samuel Livingstone, Michael Betancourt, Simon Byrne, and Mark Girolami · 2016
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The geometric foundations of Hamiltonian Monte Carlo
Michael Betancourt, Simon Byrne, Sam Livingstone, and Mark Girolami · 2017
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Khai Xiang Au, Matthew M Graham, and Alexandre H Thiery · 2020
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Andrew Gelman, Aki Vehtari, Daniel Simpson, Charles C Margossian, Bob Carpenter, Yuling Yao, Lauren Kennedy, Jonah Gabry, Paul-Christian Bürkner, and Martin Modrák · 2020
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Liberty or Depth: Deep Bayesian Neural Nets Do Not Need Complex Weight Posterior Approximations
Sebastian Farquhar, Lewis Smith, and Yarin Gal · 2020
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tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware
Junpeng Lao, Christopher Suter, Ian Langmore, Cyril Chimisov, Ashish Saxena, Pavel Sountsov, Dave Moore, Rif A Saurous, Matthew D Hoffman, and Joshua V Dillon · 2020
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A Condition Number for Hamiltonian Monte Carlo
Ian Langmore, Michael Dikovsky, Scott Geraedts, Peter Norgaard, and Rob Von Behren · 2020
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Multi-instrument Bayesian reconstruction of plasma shape evolution in the C-2W experiment
Michael Dikovsky, Edward A Baltz, Robert Von Behren, Scott Geraedts, Anton Kast, Ian Langmore, Thomas Madams, Peter Norgaard, John C Platt, Jesus Romero, Thomas Roche, Roger Smith, Erik Trask, Sean Dettrick, Hiroshi Gota, James B Titus, and Richard M Magee · 2021
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Rank-normalization, folding, and localization: An improved Rˆ for assessing convergence of MCMC (with discussion)
Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter, and Paul-Christian Bürkner · 2021
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Compiling machine learning programs via high-level tracing
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Non‐reversible parallel tempering: A scalable highly parallel MCMC scheme
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