Andrieu, Christophe, and Johannes Thoms. 2008. “A Tutorial on Adaptive MCMC.” Statistics and Computing
18 (4): 343–73.
Atchadé, Yves, Gersende Fort, Eric Moulines, and Pierre Priouret. 2011. “Adaptive Markov Chain Monte Carlo: Theory and Methods.”
In Bayesian Time Series Models
, edited by David Barber, A. Taylan Cemgil, and Silvia Chiappa, 32–51. Cambridge: Cambridge University Press.
Bales, Ben, Arya Pourzanjani, Aki Vehtari, and Linda Petzold. 2019. “Selecting the Metric in Hamiltonian Monte Carlo.” arXiv:1905.11916 [Stat]
Betancourt, Michael. 2017. “A Conceptual Introduction to Hamiltonian Monte Carlo.” arXiv:1701.02434 [Stat]
Betancourt, Michael, Simon Byrne, Sam Livingstone, and Mark Girolami. 2017. “The Geometric Foundations of Hamiltonian Monte Carlo.” Bernoulli
23 (4A): 2257–98.
Bousquet, Olivier, Ulrike von Luxburg, and Gunnar Rtsch. 2004. Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2-14, 2003, T Bingen, Germany, August 4-16, 2003, Revised Lectures. Springer.
Brosse, Nicolas, Alain Durmus, and Eric Moulines. n.d. “The Promises and Pitfalls of Stochastic Gradient Langevin Dynamics,” 11.
Calderhead, Ben. 2014. “A General Construction for Parallelizing Metropolis−Hastings Algorithms.” Proceedings of the National Academy of Sciences
111 (49): 17408–13.
Carpenter, Bob, Matthew D. Hoffman, Marcus Brubaker, Daniel Lee, Peter Li, and Michael Betancourt. 2015. “The Stan Math Library: Reverse-Mode Automatic Differentiation in C++.” arXiv Preprint arXiv:1509.07164
Caterini, Anthony L., Arnaud Doucet, and Dino Sejdinovic. 2018. “Hamiltonian Variational Auto-Encoder.”
In Advances in Neural Information Processing Systems
Chakraborty, Saptarshi, Suman K. Bhattacharya, and Kshitij Khare. 2019. “Estimating Accuracy of the MCMC Variance Estimator: A Central Limit Theorem for Batch Means Estimators.” arXiv:1911.00915 [Math, Stat]
Cornish, Robert, Paul Vanetti, Alexandre Bouchard-Côté, George Deligiannidis, and Arnaud Doucet. 2019. “Scalable Metropolis-Hastings for Exact Bayesian Inference with Large Datasets.” arXiv:1901.09881 [Cs, Stat]
Cotter, S. L., G. O. Roberts, A. M. Stuart, and D. White. 2013. “MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster.” Statistical Science
28 (3): 424–46.
Dhaka, Akash Kumar, and Alejandro Catalina. 2020. “Robust, Accurate Stochastic Optimization for Variational Inference,” 13.
Diaconis, Persi, and David Freedman. 1999. “Iterated Random Functions.” SIAM Review
1 (1): 45–76.
Durmus, Alain, and Eric Moulines. 2016. “High-Dimensional Bayesian Inference via the Unadjusted Langevin Algorithm.” arXiv:1605.01559 [Math, Stat]
Girolami, Mark, and Ben Calderhead. 2011. “Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods.” Journal of the Royal Statistical Society: Series B (Statistical Methodology)
73 (2): 123–214.
Glynn, Peter W., and Chang-Han Rhee. 2014. “Exact Estimation for Markov Chain Equilibrium Expectations.” Journal of Applied Probability
51 (A): 377–89.
Goodman, Noah, Vikash Mansinghka, Daniel Roy, Keith Bonawitz, and Daniel Tarlow. 2012. “Church: A Language for Generative Models.” arXiv:1206.3255
Goodrich, Ben, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Bob Carpenter, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. 2017. “Stan : A Probabilistic Programming Language.” Journal of Statistical Software
Hodgkinson, Liam, Robert Salomone, and Fred Roosta. 2019. “Implicit Langevin Algorithms for Sampling From Log-Concave Densities.” arXiv:1903.12322 [Cs, Stat]
Huang, Zaijing, and Andrew Gelman. 2005. “Sampling for Bayesian Computation with Large Datasets.” SSRN Electronic Journal
Jacob, Pierre E., John O’Leary, and Yves F. Atchadé. 2017. “Unbiased Markov Chain Monte Carlo with Couplings.” arXiv:1708.03625 [Stat]
Korattikara, Anoop, Yutian Chen, and Max Welling. 2015. “Sequential Tests for Large-Scale Learning.” Neural Computation
28 (1): 45–70.
Lele, Subhash R., Khurram Nadeem, and Byron Schmuland. 2010. “Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning.” Journal of the American Statistical Association
105 (492): 1617–25.
Ma, Yi-An, Tianqi Chen, and Emily B. Fox. 2015. “A Complete Recipe for Stochastic Gradient MCMC.”
In Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 2
, 2917–25. NIPS’15. Cambridge, MA, USA: MIT Press.
Mangoubi, Oren, and Aaron Smith. 2017. “Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions.” arXiv:1708.07114 [Math, Stat]
Neal, Radford M. 1993. “Probabilistic Inference Using Markov Chain Monte Carlo Methods.”
Technical Report CRGTR-93-1. Toronto Canada: Department of Computer Science, University of Toronto,.
———. 2011. “MCMC Using Hamiltonian Dynamics.”
In Handbook for Markov Chain Monte Carlo
, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng. Boca Raton: Taylor & Francis.
Propp, James Gary, and David Bruce Wilson. 1996. “Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics.”
In Random Structures & Algorithms
, 9:223–52. New York, NY, USA: John Wiley & Sons, Inc.
———. 1998. “Coupling from the Past: A User’s Guide.”
In Microsurveys in Discrete Probability
, edited by David Aldous and James Gary Propp, 41:181–92. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. Providence, Rhode Island: American Mathematical Society.
Robert, Christian P., Víctor Elvira, Nick Tawn, and Changye Wu. 2018. “Accelerating MCMC Algorithms.” WIREs Computational Statistics
10 (5): e1435.
Roberts, Gareth O., and Jeffrey S. Rosenthal. 2004. “General State Space Markov Chains and MCMC Algorithms.” Probability Surveys
1 (0): 20–71.
Roberts, G.O., and A.F.M. Smith. 1994. “Simple Conditions for the Convergence of the Gibbs Sampler and Metropolis-Hastings Algorithms.” Stochastic Processes and Their Applications
49 (2): 207–16.
Rubinstein, Reuven Y., and Dirk P. Kroese. 2016. Simulation and the Monte Carlo Method. 3 edition. Wiley series in probability and statistics. Hoboken, New Jersey: Wiley.
Rubinstein, Reuven Y., Ad Ridder, and Radislav Vaisman. 2014. Fast Sequential Monte Carlo Methods for Counting and Optimization. Wiley Series in Probability and Statistics. Hoboken, New Jersey: Wiley.
Salimans, Tim, Diederik Kingma, and Max Welling. 2015. “Markov Chain Monte Carlo and Variational Inference: Bridging the Gap.”
In Proceedings of the 32nd International Conference on Machine Learning (ICML-15)
, 1218–26. ICML’15. Lille, France: JMLR.org.
Schuster, Ingmar, Heiko Strathmann, Brooks Paige, and Dino Sejdinovic. 2017. “Kernel Sequential Monte Carlo.”
In ECML-PKDD 2017
Sisson, S. A., Y. Fan, and Mark M. Tanaka. 2007. “Sequential Monte Carlo Without Likelihoods.” Proceedings of the National Academy of Sciences
104 (6): 1760–65.
Syed, Saifuddin, Alexandre Bouchard-Côté, George Deligiannidis, and Arnaud Doucet. 2020. “Non-Reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme.” arXiv:1905.02939 [Stat]
Vehtari, Aki, Andrew Gelman, Tuomas Sivula, Pasi Jylänki, Dustin Tran, Swupnil Sahai, Paul Blomstedt, John P. Cunningham, David Schiminovich, and Christian Robert. 2019. “Expectation Propagation as a Way of Life: A Framework for Bayesian Inference on Partitioned Data.” arXiv:1412.4869 [Stat]
Wang, Xiangyu, and David B. Dunson. 2013. “Parallelizing MCMC via Weierstrass Sampler,”
Welling, Max, and Yee Whye Teh. n.d. “Bayesian Learning via Stochastic Gradient Langevin Dynamics,” 8.
Xifara, T., C. Sherlock, S. Livingstone, S. Byrne, and M. Girolami. 2014. “Langevin Diffusions and the Metropolis-Adjusted Langevin Algorithm.” Statistics & Probability Letters
91 (Supplement C): 14–19.
Xu, Kai, Hong Ge, Will Tebbutt, Mohamed Tarek, Martin Trapp, and Zoubin Ghahramani. 2019. “AdvancedHMC.jl: A Robust, Modular and Efficient Implementation of Advanced HMC Algorithms,”
Yoshida, Ryo, and Mike West. 2010. “Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing.” Journal of Machine Learning Research
11 (May): 1771–98.