Bibliography#
Effective sample size, stan manual. URL: https://mc-stan.org/docs/2_27/reference-manual/effective-sample-size-section.html.
HMC Algorithm Parameters, stan manual. URL: https://mc-stan.org/docs/2_20/reference-manual/hmc-algorithm-parameters.html.
Potential scale reduction, stan manual. URL: https://mc-stan.org/docs/2_27/reference-manual/notation-for-samples-chains-and-draws.html#potential-scale-reduction.
Abhinav Agrawal, Daniel R Sheldon, and Justin Domke. Advances in black-box vi: normalizing flows, importance weighting, and optimization. Advances in Neural Information Processing Systems, 33:17358–17369, 2020.
Jack Baker, Paul Fearnhead, Emily B Fox, and Christopher Nemeth. Control variates for stochastic gradient mcmc. Statistics and Computing, 29:599–615, 2019.
Michael Betancourt. A general metric for riemannian manifold hamiltonian monte carlo. In Geometric Science of Information: First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings, 327–334. Springer, 2013.
Michael Betancourt. A conceptual introduction to hamiltonian monte carlo. arXiv preprint arXiv:1701.02434, 2017.
Michael Betancourt, Simon Byrne, Sam Livingstone, and Mark Girolami. The geometric foundations of hamiltonian monte carlo. arXiv preprint arXiv:arXiv:1410.5110, 2017.
Sergio Blanes, Fernando Casas, and Jesús Marıa Sanz-Serna. Numerical integrators for the hybrid monte carlo method. SIAM Journal on Scientific Computing, 36(4):A1556–A1580, 2014.
James Brofos and Roy R Lederman. Evaluating the implicit midpoint integrator for riemannian hamiltonian monte carlo. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, 1072–1081. PMLR, 18–24 Jul 2021.
Tianqi Chen, Emily Fox, and Carlos Guestrin. Stochastic gradient hamiltonian monte carlo. In International conference on machine learning, 1683–1691. PMLR, 2014.
Jeremie Coullon and Christopher Nemeth. Sgmcmcjax: a lightweight jax library for stochastic gradient markov chain monte carlo algorithms. Journal of Open Source Software, 7(72):4113, 2022.
Hai-Dang Dau and Nicolas Chopin. Waste-free sequential monte carlo. arXiv preprint arXiv:2011.02328, 2020.
Wei Deng, Siqi Liang, Botao Hao, Guang Lin, and Faming Liang. Interacting contour stochastic gradient langevin dynamics. arXiv preprint arXiv:2202.09867, 2022.
Wei Deng, Guang Lin, and Faming Liang. A contour stochastic gradient langevin dynamics algorithm for simulations of multi-modal distributions. Advances in neural information processing systems, 33:15725–15736, 2020.
Nan Ding, Youhan Fang, Ryan Babbush, Changyou Chen, Robert D Skeel, and Hartmut Neven. Bayesian sampling using stochastic gradient thermostats. Advances in neural information processing systems, 2014.
Andrew Gelman, John B Carlin, Hal S Stern, and Donald B Rubin. Bayesian data analysis. Chapman and Hall/CRC, 1995.
Andrew Gelman, John B Carlin, Hal S Stern, and Donald B Rubin. Bayesian data analysis. Chapman and Hall/CRC, 2014.
Andrew Gelman and Donald B Rubin. Inference from iterative simulation using multiple sequences. Statistical science, pages 457–472, 1992.
Charles J Geyer. Practical markov chain monte carlo. Statistical science, pages 473–483, 1992.
Charles J Geyer. Introduction to markov chain monte carlo. Handbook of Markov Chain Monte Carlo, 20116022:45, 2011.
Matthew Hoffman, Alexey Radul, and Pavel Sountsov. An adaptive-mcmc scheme for setting trajectory lengths in hamiltonian monte carlo. In International Conference on Artificial Intelligence and Statistics, 3907–3915. PMLR, 2021.
Matthew D Hoffman, Andrew Gelman, and others. The no-u-turn sampler: adaptively setting path lengths in hamiltonian monte carlo. J. Mach. Learn. Res., 15(1):1593–1623, 2014.
Matthew D Hoffman and Pavel Sountsov. Tuning-free generalized hamiltonian monte carlo. In International Conference on Artificial Intelligence and Statistics, 7799–7813. PMLR, 2022.
Junpeng Lao, Christopher Suter, Ian Langmore, Cyril Chimisov, Ashish Saxena, Pavel Sountsov, Dave Moore, Rif A Saurous, Matthew D Hoffman, and Joshua V Dillon. Tfp. mcmc: modern markov chain monte carlo tools built for modern hardware. arXiv preprint arXiv:2002.01184, 2020.
Qiang Liu and Dilin Wang. Stein variational gradient descent: a general purpose bayesian inference algorithm. Advances in neural information processing systems, 2016.
Samuel Livingstone and Giacomo Zanella. The Barker Proposal: Combining Robustness and Efficiency in Gradient-Based MCMC. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(2):496–523, 01 2022. URL: https://doi.org/10.1111/rssb.12482, arXiv:https://academic.oup.com/jrsssb/article-pdf/84/2/496/49322274/jrsssb\_84\_2\_496.pdf, doi:10.1111/rssb.12482.
Xiaoyu Lu, Valerio Perrone, Leonard Hasenclever, Yee Whye Teh, and Sebastian Vollmer. Relativistic monte carlo. In Artificial Intelligence and Statistics, 1236–1245. PMLR, 2017.
Yi-An Ma, Tianqi Chen, and Emily Fox. A complete recipe for stochastic gradient mcmc. Advances in neural information processing systems, 2015.
Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.
Iain Murray, Ryan Adams, and David MacKay. Elliptical slice sampling. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, 541–548. JMLR Workshop and Conference Proceedings, 2010.
Radford M Neal. Non-reversibly updating a uniform [0, 1] value for metropolis accept/reject decisions. arXiv preprint arXiv:2001.11950, 2020.
Kirill Neklyudov and Max Welling. Orbital mcmc. In International Conference on Artificial Intelligence and Statistics, 5790–5814. PMLR, 2022.
Yurii Nesterov. Primal-dual subgradient methods for convex problems. Mathematical programming, 120(1):221–259, 2009.
IP Omelyan, IM Mryglod, and R Folk. Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations. Computer Physics Communications, 151(3):272–314, 2003.
Du Phan, Neeraj Pradhan, and Martin Jankowiak. Composable effects for flexible and accelerated probabilistic programming in numpyro. arXiv preprint arXiv:1912.11554, 2019.
Herbert Robbins and Sutton Monro. A stochastic approximation method. The annals of mathematical statistics, pages 400–407, 1951.
Geoffrey Roeder, Yuhuai Wu, and David K Duvenaud. Sticking the landing: simple, lower-variance gradient estimators for variational inference. Advances in Neural Information Processing Systems, 2017.
Tetsuya Takaishi and Philippe De Forcrand. Testing and tuning symplectic integrators for the hybrid monte carlo algorithm in lattice qcd. Physical Review E, 73(3):036706, 2006.
Michalis K Titsias and Omiros Papaspiliopoulos. Auxiliary gradient-based sampling algorithms. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 80(4):749–767, 2018.
Guanyang Wang. Exact convergence analysis of the independent metropolis-hastings algorithms. Bernoulli, 28(3):2012–2033, 2022.
Lu Zhang, Bob Carpenter, Andrew Gelman, and Aki Vehtari. Pathfinder: parallel quasi-newton variational inference. Journal of Machine Learning Research, 23(306):1–49, 2022.