The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo

Journal of Machine Learning Research

Volumn 15, Issue , 2014, Pages 1593-1623

  Hoffman, Matthew D ^a   Gelman, Andrew ^b  

^a ADOBE RESEARCH   (United States)

^b Department of Statistics and Political Science Columbia University ^*  (United States)

Author keywords

Adaptive Monte Carlo; Bayesian inference; Dual averaging; Hamiltonian Monte Carlo; Markov chain Monte Carlo

Indexed keywords

BAYESIAN NETWORKS; HAMILTONIANS; INFERENCE ENGINES; MONTE CARLO METHODS; PARAMETER ESTIMATION; RANDOM PROCESSES;

AUTOMATIC INFERENCE; BAYESIAN INFERENCE; CORRELATED PARAMETERS; DUAL AVERAGING; GRADIENT INFORMATIONS; MARKOV CHAIN MONTE CARLO ALGORITHMS; MARKOV CHAIN MONTE-CARLO; RECURSIVE ALGORITHMS;

ALGORITHMS;

EID: 84901687683     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. C. Andrieu and J. Thoms. A tutorial on adaptive MCMC. Statistics and Computing, 18 (4):343-373, 2008.
2. A. Beskos, N. Pillai, G. Roberts, J. Sanz-Serna, and A. Stuart. Optimal tuning of the hybrid monte-carlo algorithm. Arxiv preprint arXiv:1001.4460, 2010.
3. M. Betancourt. Generalizing the no-U-turn sampler to Riemannian manifolds. ArXiv preprint arXiv:1304.1920, 2013.
4. M. Creutz. Global Monte Carlo algorithms for many-fermion systems. Physical Review D, 38(4):1228-1238, 1988.
5. H. Daume III. HBC: Hierarchical Bayes compiler, 2007. URL http://hal3.name/HBC.
6. A. Duane, A. Kennedy, B. Pendleton, and D. Roweth. Hybrid Monte Carlo. Physics Letters B, 195(2):216-222, 1987.
7. A. Frank and A. Asuncion. UCI machine learning repository, 2010. URL http://archive. ics.uci.edu/ml.
8. A. Gelman, G. Roberts, and W. Gilks. Efficient Metropolis jumping rules. Bayesian Statistics, 5:599-608, 1996.
9. A. Gelman, J. Carlin, H. Stern, and D. Rubin. Bayesian Data Analysis. Chapman & Hall, 2004.
10. S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6:721-741, 1984. (Pubitemid 15453722)
11. W. Gilks and D. Spiegelhalter. A language and program for complex Bayesian modelling. The Statistician, 3:169-177, 1992.
12. M. Girolami and B. Calderhead. Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73 (2):123-214, 2011.
13. A. Griewank and A. Walther. Evaluating Derivatives: Principles and Techniques of Algo rithmic Differentiation. Society for Industrial and Applied Mathematics (SIAM), 2008.
14. S. Lan, V. Stathopoulos, B. Shahbaba, and M. Girolami. Lagrangian Dynamical Monte Carlo. ArXiv preprint arXiv:1211.3759, 2012.
15. B. Leimkuhler and S. Reich. Simulating Hamiltonian Dynamics, volume 14. Cambridge University Press, 2004.
16. N. Metropolis, A. Rosenbluth, M. Rosenbluth, M. Teller, and E. Teller. Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087-1092, 1953.
17. T. Minka, J. Winn, J. Guiver, and D. Knowles. Infer.NET 2.4, Microsoft Research Cambridge, 2010., utl=http://research.microsoft.com/infernet.
18. R. Neal. Probabilistic inference using Markov chain Monte Carlo methods. Technical Report CRG-TR-93-1, Department of Computer Science, University of Toronto, 1993.
19. R. Neal. An improved acceptance procedure for the hybrid Monte Carlo algorithm. Journal of Computational Physics, 111:194-203, 1994. (Pubitemid 124013390)
20. R. Neal. Slice sampling. Annals of Statistics, 31(3):705-741, 2003. (Pubitemid 38640403)
21. R. Neal. Handbook of Markov Chain Monte Carlo, chapter 5: MCMC Using Hamiltonian Dynamics. CRC Press, 2011.
22. Y. Nesterov. Primal-dual subgradient methods for convex problems. Mathematical Programming, 120(1):221-259, 2009.
23. A. Patil, D. Huard, and C. Fonnesbeck. PyMC: Bayesian stochastic modelling in python. Journal of Statistical Software, 35(4):1-81, 2010.
24. M. Plummer. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling, 2003. URL http://sourceforge.net/projects/mcmc-jags/.
25. M. Plummer, N. Best, K. Cowles, and K. Vines. CODA: Convergence diagnosis and output analysis for MCMC. R News, 6(1):7-11, March 2006.
26. H. Robbins and S. Monro. A stochastic approximation method. The Annals of Mathematical Statistics, pages 400-407, 1951.
27. Stan Development Team. Stan: A C++ library for probability and sampling, version 1.1, 2013. URL http://mc-stan.org/.
28. L. Tierney and A. Mira. Some adaptive Monte Carlo methods for Bayesian inference. Statistics in Medicine, 18:2507-2515, 1999. (Pubitemid 29423512)
29. M. Wainwright and M. Jordan. Graphical models, exponential families, and variational inference. Foundations and Trends in Machine Learning, 1(1-2):1-305, 2008.