The Apogee to Apogee Path Sampler

References

• Beskos, A., Pillai, N., Roberts, G., Sanz-Serna, J.-M. and Stuart, A. (2013), “Optimal Tuning of the Hybrid Monte Carlo Algorithm,” Bernoulli, 19, 1501–1534. http://www.jstor.org/stable/42919328. DOI: 10.3150/12-BEJ414.
   Web of Science ®Google Scholar
• Bou-Rabee, N., and Sanz-Serna, J. M. (2017), “Randomized Hamiltonian Monte Carlo,” The Annals of Applied Probability, 27, 2159–2194. http://www.jstor.org/stable/26361544. DOI: 10.1214/16-AAP1255.
   Web of Science ®Google Scholar
• Brooks, S., Gelman, A., Jones, G. L. and Meng, X.-L., ds. (2011), Handbook of Markov Chain Monte Carlo, Chapman & Hall/CRC Handbooks of Modern Statistical Methods, Boca Raton, FL: CRC Press.
   Google Scholar
• Duane, S., Kennedy, A., Pendleton, B. J., and Roweth, D. (1987), “Hybrid Monte Carlo,” Physics Letters B, 195, 216–222. https://www.sciencedirect.com/science/article/pii/037026938791197X. DOI: 10.1016/0370-2693(87)91197-X.
   Web of Science ®Google Scholar
• Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (1996), Markov Chain Monte Carlo in Practice, London, UK: Chapman and Hall.
   Google Scholar
• Girolami, M., and Calderhead, B. (2011), “Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods,” Journal of the Royal Statistical Society, Series B, 73, 123–214. DOI: 10.1111/j.1467-9868.2010.00765.x.
   Google Scholar
• Heng, J., and Jacob, P. E. (2019), “Unbiased Hamiltonian Monte Carlo with Couplings,” Biometrika, 106, 287–302. DOI: 10.1093/biomet/asy074.
   Web of Science ®Google Scholar
• Hoffman, M., Radul, A., and Sountsov, P. (2021), “An Adaptive-MCMC Scheme for Setting Trajectory Lengths in Hamiltonian Monte Carlo,” in Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, eds., A. Banerjee and K. Fukumizu, vol. 130 of Proceedings of Machine Learning Research, pp. 3907–3915. PMLR. https://proceedings.mlr.press/v130/hoffman21a.html.
   Google Scholar
• Hoffman, M. D., and Gelman, A. (2014), “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo,” Journal of Machine Learning Research, 15, 1593–1623.
   Web of Science ®Google Scholar
• Horowitz, A. M. (1991), “A Generalized Guided Monte Carlo Algorithm,” Physics Letters B, 268, 247–252. https://www.sciencedirect.com/science/article/pii/0370269391908125. DOI: 10.1016/0370-2693(91)90812-5.
   Web of Science ®Google Scholar
• Livingstone, S., Faulkner, M. F., and Roberts, G. O. (2019), “Kinetic Energy Choice in Hamiltonian/Hybrid Monte Carlo,” Biometrika, 106, 303–319. DOI: 10.1093/biomet/asz013.
   Web of Science ®Google Scholar
• Mackenze, P. B. (1989), “An Improved Hybrid Monte Carlo Method,” Physics Letters B, 226, 369–371. DOI: 10.1016/0370-2693(89)91212-4.
   Web of Science ®Google Scholar
• Neal, R. M. (1992), “An Improved Acceptance Procedure for the Hybrid Monte Carlo Algorithm,” Journal of Computational Physics, 111, 194–203. DOI: 10.1006/jcph.1994.1054.
   Web of Science ®Google Scholar
• Neal, R. M. (2011a), “MCMC Using Ensembles of States for Problems with Fast and Slow Variables such as Gaussian Process Regression.” arXiv 1101.0387.
   Google Scholar
• Neal, R. M. (2011b), “MCMC Using Hamiltonian Dynamics,” in Handbook of Markov Chain Monte Carlo, eds. S. Brooks, A. Gelman, G. Jones and X.-L. Meng), pp. 113–162, Boca Raton, FL: CRC press.
   Google Scholar
• Pagani, F., Wiegand, M., and Nadarajah, S. (2021), “An n-dimensional Rosenbrock Distribution for Markov Chain Monte Carlo Testing,” Scandinavian Journal of Statistics, 49, 657–680. DOI: 10.1111/sjos.12532.
   Web of Science ®Google Scholar
• Roberts, G. O., and Rosenthal, J. S. (2001), “Optimal Scaling for Various Metropolis-Hastings Algorithms,” Statistical Science, 16, 351–367. DOI: 10.1214/ss/1015346320.
   Web of Science ®Google Scholar
• Rosenbrock, H. H. (1960), “An Automatic Method for Finding the Greatest or Least Value of a Function,” The Computer Journal, 3, 175–184. DOI: 10.1093/comjnl/3.3.175.
   Web of Science ®Google Scholar
• Salvatier, J., Wiecki, T. V., and Fonnesbeck, C. (2016), “Probabilistic Programming in Python Using PyMC3,” PeerJ Computer Science, 2, e55. DOI: 10.7717/peerj-cs.55.
   Google Scholar
• Sherlock, C., and Roberts, G. (2009), “Optimal Scaling of the Random Walk Metropolis on Elliptically Symmetric Unimodal Targets,” Bernoulli, 15, 774–798. DOI: 10.3150/08-BEJ176.
   Web of Science ®Google Scholar
• Stan Development Team. (2020), Stan Modeling Language Users Guide and Reference Manual, Version 2.28, http://mc-stan.org/.
   Google Scholar
• Wu, C., Stoehr, J., and Robert, C. P. (2019), “Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale.” arXiv 1810.04449.
   Google Scholar
• Ylvisaker, N. D. (1965), “The Expected Number of Zeros of a Stationary Gaussian Process,” Annals of Mathematical Statistics, 36, 1043–1046. DOI: 10.1214/aoms/1177700077.
   Google Scholar