This is an old version, view current version.

References

Betancourt, Michael. 2010. “Cruising the Simplex: Hamiltonian Monte Carlo and the Dirichlet Distribution.” arXiv 1010.3436. http://arxiv.org/abs/1010.3436.
———. 2016a. “Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo.” arXiv 1604.00695. https://arxiv.org/abs/1604.00695.
———. 2016b. “Identifying the Optimal Integration Time in Hamiltonian Monte Carlo.” arXiv 1601.00225. https://arxiv.org/abs/1601.00225.
———. 2017. “A Conceptual Introduction to Hamiltonian Monte Carlo.” arXiv 1701.02434. https://arxiv.org/abs/1701.02434.
Betancourt, Michael, and Mark Girolami. 2013. Hamiltonian Monte Carlo for Hierarchical Models.” arXiv 1312.0906. http://arxiv.org/abs/1312.0906.
Corden, Martyn J., and David Kreitzer. 2014. “Consistency of Floating-Point Results Using the Intel Compiler or Why Doesn’t My Application Always Give the Same Answer?” Intel Corporation. https://software.intel.com/en-us/articles/consistency-of-floating-point-results-using-the-intel-compiler.
Duchi, John, Elad Hazan, and Yoram Singer. 2011. “Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.” The Journal of Machine Learning Research 12: 2121–59.
Gelman, Andrew, J. B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis. Third Edition. London: Chapman & Hall / CRC Press.
Gelman, Andrew, and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel-Hierarchical Models. Cambridge, United Kingdom: Cambridge University Press.
Gelman, Andrew, and Donald B. Rubin. 1992. “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7 (4): 457–72.
Geyer, Charles J. 1992. “Practical Markov Chain Monte Carlo.” Statistical Science, 473–83.
Geyer, Charles J. 2011. “Introduction to Markov Chain Monte Carlo.” In Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng, 3–48. Chapman; Hall/CRC.
Hoffman, Matthew D., and Andrew Gelman. 2014. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” Journal of Machine Learning Research 15: 1593–623. http://jmlr.org/papers/v15/hoffman14a.html.
Kucukelbir, Alp, Dustin Tran, Rajesh Ranganath, Andrew Gelman, and David M Blei. 2017. “Automatic Differentiation Variational Inference.” Journal of Machine Learning Research.
Leimkuhler, Benedict, and Sebastian Reich. 2004. Simulating Hamiltonian Dynamics. Cambridge: Cambridge University Press.
Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. 2009. “Generating Random Correlation Matrices Based on Vines and Extended Onion Method.” Journal of Multivariate Analysis 100: 1989–2001.
Metropolis, N., A. Rosenbluth, M. Rosenbluth, M. Teller, and E. Teller. 1953. “Equations of State Calculations by Fast Computing Machines.” Journal of Chemical Physics 21: 1087–92.
Muller, Mervin E. 1959. “A Note on a Method for Generating Points Uniformly on n-Dimensional Spheres.” Commun. ACM 2 (4): 19–20. https://doi.org/10.1145/377939.377946.
Neal, Radford. 2011. MCMC Using Hamiltonian Dynamics.” In Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng, 116–62. Chapman; Hall/CRC.
Nesterov, Y. 2009. “Primal-Dual Subgradient Methods for Convex Problems.” Mathematical Programming 120 (1): 221–59.
Nocedal, Jorge, and Stephen J. Wright. 2006. Numerical Optimization. Second. Berlin: Springer-Verlag.
Roberts, G. O., Andrew Gelman, and Walter R. Gilks. 1997. “Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms.” Annals of Applied Probability 7 (1): 110–20.
Zhang, Lu, Bob Carpenter, Andrew Gelman, and Aki Vehtari. 2022. “Pathfinder: Parallel Quasi-Newton Variational Inference.” Journal of Machine Learning Research 23 (306): 1–49. http://jmlr.org/papers/v23/21-0889.html.