Andrieu,, C., & Doucet,, A. (2002). Particle filtering for partially observed Gaussian state space models. Journal of Royal Statistical Society Series B, 64, 827–836.

Andrieu,, C., Doucet,, A., & Holenstein,, R. (2011). Particle Markov chain Monte Carlo (with discussion). Journal of Royal Statistical Society Series B, 72(2), 269–342.

Andrieu,, C., & Roberts,, G. (2009). The pseudo‐marginal approach for efficient Monte Carlo computations. The Annals of Statistics, 37, 697–725.

Angelino,, E., Kohler,, E., Waterland,, A., Seltzer,, M., & Adams,, R. (2014). Accelerating MCMC via parallel predictive prefetching. *arXiv preprint arXiv:1403.7265*.

Aslett,, L., Esperança,, P., & Holmes,, C. (2015). A review of homomorphic encryption and software tools for encrypted statistical machine learning. arXiv preprint arXiv:1508.06574.

Atchadé,, Y. F., & Liu,, J. S. (2004). The Wang‐Landau algorithm for Monte Carlo computation in general state spaces. Statistica Sinica, 20, 209–233.

Atchadé,, Y. F., Roberts,, G., & Rosenthal,, J. (2011). Towards optimal scaling of Metropolis‐coupled Markov chain Monte Carlo. Statistics and Computing, 21, 555–568.

Banterle,, M., Grazian,, C., Lee,, A., & Robert,, C. P. (2015). Accelerating Metropolis–Hastings algorithms by delayed acceptance. *arXiv preprint arXiv:1503.00996*.

Bardenet,, R., Doucet,, A., & Holmes,, C. (2014). Towards scaling up Markov chain Monte Carlo: An adaptive subsampling approach. Paper presented at International Conference on Machine Learning (ICML), 405–413.

Bardenet,, R., Doucet,, A., & Holmes,, C. (2015). On Markov chain Monte Carlo methods for tall data. *arXiv preprint arXiv:1505.02827*.

Bédard,, M., Douc,, R., & Moulines,, E. (2012). Scaling analysis of multiple‐try MCMC methods. Stochastic Processes and their Applications, 122, 758–786.

Betancourt,, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo. *ArXiv e‐prints: 1701.02434*.

Bhatnagar,, N., & Randall,, D. (2016). Simulated tempering and swapping on mean‐field models. Journal of Statistical Physics, 164, 495–530.

Bierkens,, J. (2016). Non‐reversible Metropolis‐Hastings. Statistics and Computing, 26, 1213–1228.

Bierkens,, J., Bouchard‐Côté,, A., Doucet,, A., Duncan,, A. B., Fearnhead,, P., Roberts,, G., & Vollmer,, S. J. (2017). Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains. *arXiv preprint arXiv:1701.04244*.

Bierkens,, J., Fearnhead,, P., & Roberts,, G. (2016). The zig‐zag process and super‐efficient sampling for Bayesian analysis of big data. *arXiv preprint arXiv:1607.03188*.

Bou‐Rabee,, N., Sanz‐Serna,, J. M., et al. (2017). Randomized Hamiltonian Monte Carlo. The Annals of Applied Probability, 27, 2159–2194.

Bouchard‐Côté,, A., Vollmer,, S. J., & Doucet,, A. (2017). The bouncy particle sampler: A non‐reversible rejection‐free Markov chain Monte Carlo method. Journal of the American Statistical Association, To appear.

Calderhead,, B. (2014). A general construction for parallelizing Metropolis–Hastings algorithms. Proceedings of the National Academy of Sciences, 111, 17408–17413.

Cappé,, O., Douc,, R., Guillin,, A., Marin,, J.‐M., & Robert,, C. (2008). Adaptive importance sampling in general mixture classes. Statistics and Computing, 18, 447–459.

Cappé,, O., Guillin,, A., Marin,, J.‐M., & Robert,, C. (2004). Population Monte Carlo. Journal of Computational and Graphical Statistics, 13, 907–929.

Cappé,, O., & Robert,, C. (2000). Ten years and still running! Journal of American Statistical Association, 95, 1282–1286.

Carpenter,, B., Gelman,, A., Hoffman,, M., Lee,, D., Goodrich,, B., Betancourt,, M., … Riddell,, A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76.

Carter,, J., & White,, D. (2013). History matching on the Imperial College fault model using parallel tempering. Computational Geosciences, 17, 43–65.

Casella,, G., & Robert,, C. (1996). Rao‐Blackwellization of sampling schemes. Biometrika, 83, 81–94.

Chen,, T., Fox,, E., & Guestrin,, C. (2014). Stochastic gradient Hamiltonian Monte Carlo. In Proceedings of the International Conference on Machine Learning, ICML`2014 (pp. 1683–1691).

Chen,, T., & Hwang,, C. (2013). Accelerating reversible Markov chains. Statistics %26 Probability Letters, 83, 1956–1962.

Davis,, M. H. (1984). Piecewise‐deterministic Markov processes: A general class of non‐diffusion stochastic models. Journal of the Royal Statistical Society: Series B: Methodological, 353–388.

Davis,, M. H. (1993). Markov models %26 optimization (Vol. 49). CRC Press.

Del Moral,, P., Doucet,, A., & Jasra,, A. (2006). Sequential Monte Carlo samplers. Journal of Royal Statistical Society Series B, 68, 411–436.

Deligiannidis,, G., Doucet,, A., & Pitt,, M. K. (2015). The correlated pseudo‐marginal method. *arXiv preprint arXiv:1511.04992*.

Ding,, N., Fang,, Y., Babbush,, R., Chen,, C., Skeel,, R. D., & Neven,, H. (2014). Bayesian sampling using stochastic gradient thermostats. Proceedings of the 27th International Conference on Neural Information Processing Systems ‐ Volume 2, NIPS 2015 (pp. 3203–3211).

Douc,, R., Guillin,, A., Marin,, J.‐M., & Robert,, C. (2007). Convergence of adaptive mixtures of importance sampling schemes. Annals of Statistics, 35(1), 420–448.

Douc,, R., & Robert,, C. (2010). A vanilla variance importance sampling via population Monte Carlo. Annals of Statistics, 39(1), 261–277.

Doucet,, A., Godsill,, S., & Andrieu,, C. (2000). On sequential Monte‐Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, 197–208.

Duane,, S., Kennedy,, A. D., Pendleton,, B. J., & Roweth,, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195, 216–222.

Durmus,, A., & Moulines,, E. (2017). Nonasymptotic convergence analysis for the unadjusted Langevin algorithm. Annals of Applied Probability, 27, 1551–1587.

Earl,, D. J., & Deem,, M. W. (2005). Parallel tempering: Theory, applications, and new perspectives. Physical Chemistry Chemical Physics, 7, 3910–3916.

Fielding,, M., Nott,, D. J., & Liong,, S.‐Y. (2011). Efficient MCMC schemes for computationally expensive posterior distributions. Technometrics, 53, 16–28.

Gelfand,, A., & Smith,, A. (1990). Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.

Gelman,, A., Gilks,, W., & Roberts,, G. (1996). Efficient Metropolis jumping rules. In J. Berger,, J. Bernardo,, A. Dawid,, D. Lindley,, & A. Smith, (Eds.), Bayesian statistics 5 (pp. 599–608). Oxford, England: Oxford University Press.

Geyer,, C. J. (1991). Markov chain Monte Carlo maximum likelihood. Computing Science and Statistics, 23, 156–163.

Girolami,, M., & Calderhead,, B. (2011). Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 73, 123–214.

Guihenneuc‐Jouyaux,, C., & Robert,, C. P. (1998). Discretization of continuous Markov chains and Markov chain Monte Carlo convergence assessment. Journal of the American Statistical Association, 93, 1055–1067.

Haario,, H., Saksman,, E., & Tamminen,, J. (1999). Adaptive proposal distribution for random walk Metropolis algorithm. Computational Statistics, 14(3), 375–395.

Hoffman,, M. D., & Gelman,, A. (2014). The No‐U‐turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning and Research, 15, 1593–1623.

Hwang,, C.‐R., Hwang‐Ma,, S.‐Y., & Sheu,, S.‐J. (1993). Accelerating gaussian diffusions. The Annals of Applied Probability, 3, 897–913.

Iba,, Y. (2000). Population‐based Monte Carlo algorithms. Transactions of the Japanese Society for Artificial Intelligence, 16, 279–286.

Jacob,, P. E., O`Leary,, J., & Atchadé,, Y. F. (2017). Unbiased Markov chain Monte Carlo with couplings. ArXiv e‐prints. 1708.03625.

Jacob,, P., Robert,, C. P., & Smith,, M. H. (2011). Using parallel computation to improve independent Metropolis–Hastings based estimation. Journal of Computational and Graphical Statistics, 20, 616–635.

Lehmann,, E., & Casella,, G. (1998). Theory of point estimation (revised ed.). New York, NY: Springer‐Verlag.

Liang,, F., Liu,, C., & Carroll,, R. (2007). Stochastic approximation in Monte Carlo computation. Journal of the American Statistical Association, 102, 305–320.

Liu,, J., Wong,, W., & Kong,, A. (1994). Covariance structure of the Gibbs sampler with application to the comparison of estimators and augmentation schemes. Biometrika, 81, 27–40.

Liu,, J., Wong,, W., & Kong,, A. (1995). Covariance structure and convergence rates of the Gibbs sampler with various scans. Journal of Royal Statistical Society Series B, 57, 157–169.

Liu,, J. S., Liang,, F., & Wong,, W. H. (2000). The multiple‐try method and local optimization in Metropolis sampling. Journal of the American Statistical Association, 95, 121–134.

Livingstone,, S., Faulkner,, M. F., & Roberts,, G. O. (2017). Kinetic energy choice in Hamiltonian/hybrid Monte Carlo. *arXiv preprint arXiv:1706.02649*.

MacKay,, D. J. C. (2002). Information theory, inference %26 learning algorithms. Cambridge, England: Cambridge University Press.

Marinari,, E., & Parisi,, G. (1992). Simulated tempering: A new Monte Carlo scheme. EPL (Europhysics Letters), 19, 451–458.

Martino,, L., Elvira,, V., Luengo,, D., Corander,, J., & Louzada,, F. (2016). Orthogonal parallel MCMC methods for sampling and optimization. Digital Signal Processing, 58, 64–84.

Martino,, L. (2018). A Review of Multiple Try MCMC algorithms for Signal Processing. ArXiv e‐prints. 1801.09065.

Mengersen,, K., & Robert,, C. (2003). Iid sampling with self‐avoiding particle filters: The pinball sampler. In J. Bernardo,, M. Bayarri,, J. Berger,, A. Dawid,, D. Heckerman,, A. Smith,, & M. West, (Eds.), Bayesian statistics (Vol. 7). Oxford, England: Oxford University Press.

Meyn,, S., & Tweedie,, R. (1993). Markov chains and stochastic stability. New York, NY: Springer‐Verlag.

Miasojedow,, B., Moulines,, E., & Vihola,, M. (2013). An adaptive parallel tempering algorithm. Journal of Computational and Graphical Statistics, 22, 649–664.

Minsker,, S., Srivastava,, S., Lin,, L., & Dunson,, D. B. (2014). Scalable and robust Bayesian inference via the median posterior. In Proceedings of the 31st International Conference on International Conference on Machine Learning ‐ Volume 32 (pp. 1656–1664). ICML`14, JMLR.org.

Mira,, A. (2001). On Metropolis‐Hastings algorithms with delayed rejection. Metron, 59(3–4), 231–241.

Mira,, A., & Sargent,, D. J. (2003). A new strategy for speeding Markov chain Monte Carlo algorithms. Statistical Methods and Applications, 12, 49–60.

Mohamed,, L., Calderhead,, B., Filippone,, M., Christie,, M., & Girolami,, M. (2012). Population MCMC methods for history matching and uncertainty quantification. Computational Geosciences, 16, 423–436.

Mykland,, P., Tierney,, L., & Yu,, B. (1995). Regeneration in Markov chain samplers. Journal of the American Statistical Association, 90, 233–241.

Neal,, R. M. (1996). Sampling from multimodal distributions using tempered transitions. Statistics and Computing, 6, 353–366.

Neal,, R. (1999). Bayesian learning for neural networks (Vol. 118). New York, NY: Springer Verlag Lecture notes.

Neal,, R. (2011). MCMC using Hamiltonian dynamics. In S. Brooks,, A. Gelman,, G. L. Jones,, & X.‐L. Meng, (Eds.), Handbook of Markov Chain Monte Carlo (pp. 113–162). New York, NY: CRC Press.

Neiswanger,, W., Wang,, C., & Xing,, E. (2013). Asymptotically exact, embarrassingly parallel MCMC. *arXiv preprint arXiv:1311.4780*.

Quiroz,, M., Villani,, M., & Kohn,, R. (2016). Exact subsampling MCMC. *arXiv preprint arXiv:1603.08232*.

Rasmussen,, C. E. (2003). Gaussian processes to speed up hybrid Monte Carlo for expensive Bayesian integrals. In J. Bernardo,, M. Bayarri,, J. Berger,, A. Dawid,, D. Heckerman,, A. Smith,, & M. West, (Eds.), Bayesian Statistics (Vol. 7, pp. 651–659). Oxford, England: Oxford University Press.

Rasmussen,, C. E., & Williams,, C. K. I. (2005). Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). Cambridge, MA: The MIT Press.

Rhee,, C.‐H., & Glynn,, P. W. (2015). Unbiased estimation with square root convergence for sde models. Operations Research, 63, 1026–1043.

Robert,, C., & Casella,, G. (2004). Monte Carlo statistical methods (2nd ed.). New York, NY: Springer‐Verlag.

Robert,, C., & Casella,, G. (2009). Introducing Monte Carlo methods with R. New York: Springer‐Verlag.

Roberts,, G., Gelman,, A., & Gilks,, W. R. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. The Annals of Applied Probability, 7, 110–120.

Roberts,, G., & Rosenthal,, J. (2001). Optimal scaling for various Metropolis‐Hastings algorithms. Statistical Science, 16, 351–367.

Roberts,, G., & Rosenthal,, J. (2007). Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms. Journal of Applied Probability, 44(2), 458–475.

Roberts,, G., & Rosenthal,, J. (2009). Examples of adaptive MCMC. Journal of Computational and Graphical Statistics, 18, 349–367.

Roberts,, G., & Rosenthal,, J. (2014). Minimising MCMC variance via diffusion limits, with an application to simulated tempering. The Annals of Applied Probability, 24, 131–149.

Rubinstein,, R. Y. (1981). Simulation and the Monte Carlo method. New York, NY: John Wiley.

Saksman,, E., & Vihola,, M. (2010). On the ergodicity of the adaptive Metropolis algorithm on unbounded domains. The Annals of Applied Probability, 20(6), 2178–2203.

Scott,, S. L., Blocker,, A. W., Bonassi,, F. V., Chipman,, H. A., George,, E. I., & McCulloch,, R. E. (2016). Bayes and big data: The consensus Monte Carlo algorithm. International Journal of Management Science and Engineering Management, 11, 78–88.

Srivastava,, S., Cevher,, V., Dinh,, Q., & Dunson,, D. (2015). WASP: Scalable Bayes via barycenters of subset posteriors. In G. Lebanon, and S. V. N. Vishwanathan, (Eds.), Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, (pp. 912–920) vol. 38 of Proceedings of Machine Learning Research. PMLR, San Diego, California, USA.

Storvik,, G. (2002). Particle filters for state space models with the presence of static parameters. IEEE Transactions on Signal Processing, 50, 281–289.

Sun,, Y., Gomez,, F., & Schmidhuber,, J. (2010). Improving the asymptotic performance of Markov chain Monte Carlo by inserting vortices. In Proceedings of the 23rd International Conference on Neural Information Processing Systems ‐ Volume 2 (pp. 2235–2243). NIPS`10, Curran Associates Inc., USA.

Terenin,, A., Simpson,, D., & Draper,, D. (2015). Asynchronous Gibbs Sampling. ArXiv e‐prints. 1509.08999.

Tierney,, L., & Mira,, A. (1998). Some adaptive Monte Carlo methods for Bayesian inference. Statistics in Medicine, 18, 2507–2515.

Tjelmeland,, H. (2004). *Using all Metropolis‐Hastings proposals to estimate mean values*. (Technical Report 4). Norwegian University of Science and Technology, Trondheim, Norway.

Wang,, F., & Landau,, D. (2001). Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram. Physical Review E, 64, 056101.

Wang,, X. & Dunson,, D. (2013). Parallelizing MCMC via weierstrass sampler. *arXiv preprint arXiv:1312.4605*.

Wang,, X., Guo,, F., Heller,, K., & Dunson,, D. (2015). Parallelizing MCMC with random partition trees. Advances in Neural Information Processing Systems, 451–459.

Welling,, M. & Teh,, Y. (2011). Bayesian learning via stochastic gradient Langevin dynamics. In Proceedings of the 28th International Conference on International Conference on Machine Learning. ICML`11 (pp. 681–688), USA: Omnipress.

Woodard,, D. B., Schmidler,, S. C., & Huber,, M. (2009a). Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions. The Annals of Applied Probability, 19, 617–640.

Woodard,, D. B., Schmidler,, S. C., & Huber,, M. (2009b). Sufficient conditions for torpid mixing of parallel and simulated tempering. Electronic Journal of Probability, 14, 780–804.

Xie,, Y., Zhou,, J., & Jiang,, S. (2010). Parallel tempering Monte Carlo simulations of lysozyme orientation on charged surfaces. The Journal of Chemical Physics, 132. 02B602.