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Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes.
Simulation of nonhomogeneous Poisson processes by thinning
Lewis, P. A. W. and Shedler, G. S. (1979) · 1979
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Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models
Davis, M. H. (1984) · 1984
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Markov models and optimization
Davis, M. H. A. (1993) · 1993
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Blind deconvolution via sequential imputations
Liu, J. S. and Chen, R. (1995) · 1995
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Monte Carlo filter and smoother for non-Gaussian nonlinear state space models
Kitagawa, G. (1996) · 1996
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A guided walk Metropolis algorithm
Gustafson, P. (1998) · 1998
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Sequential Monte Carlo methods for dynamic systems
Liu, J. S. and Chen, R. (1998) · 1998
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Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation
Neal, R. M. (1998) · 1998
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An improved particle filter for non-linear problems
Carpenter, J., Clifford, P., and Fearnhead, P. (1999) · 1999
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Analysis of a nonreversible Markov chain sampler
Diaconis, P., Holmes, S., and Neal, R. (2000) · 2000
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On sequential Monte Carlo sampling methods for Bayesian filtering
Doucet, A., Godsill, S. J., and Andrieu, C. (2000) · 2000
Earlier work this paper cites.
On the stability of interacting processes with applications to filtering and genetic algorithms
Del Moral, P. and Guionnet, A. (2001) · 2001
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Quantum Monte Carlo simulations of solids
Foulkes, W., Mitas, L., Needs, R., and Rajagopal, G. (2001) · 2001
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Improving Asymptotic Variance of MCMC Estimators: Non-reversible Chains are Better
Neal, R. M. (2004) · 2004
Earlier work this paper cites.
Exact simulation of diffusions
Beskos, A. and Roberts, G. O. (2005) · 2005
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Markov Processes: Characterization and Convergence (Wiley Series in Probability and Statistics)
Ethier, S. N. and Kurtz, T. G. (2005) · 2005
Cited alongside, same era.
Retrospective exact simulation of diffusion sample paths with applications
Beskos, A., Papaspiliopoulos, O., and Roberts, G. O. (2006) · 2006
Cited alongside, same era.
A factorisation of diffusion measure and finite sample path constructions
Beskos, A., Papaspiliopoulos, O., and Roberts, G. O. (2008) · 2008
Cited alongside, same era.
Simulation of Brownian motion at first passage times
Burq, Z. and Jones, O. (2008) · 2008
Cited alongside, same era.
Particle filters for partially-observed diffusions
Fearnhead, P., Papaspiliopoulos, O., and Roberts, G. O. (2008) · 2008
Cited alongside, same era.
The pseudo-marginal approach for efficient Monte Carlo computations
Andrieu, C. and Roberts, G. O. (2009) · 2009
Long-term stability of sequential Monte Carlo methods under verifiable conditions
Douc, R., Moulines, E., Olsson, J., et al. (2014) · 2014
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On Markov chain Monte Carlo methods for tall data
Bardenet, R., Doucet, A., and Holmes, C. (2015) · 2015
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Non-reversible Metropolis-Hastings
Bierkens, J. (2015) · 2015
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A piecewise deterministic scaling limit of Lifted Metropolis-Hastings in the Curie-Weiss model
Bierkens, J. and Roberts, G. (2015) · 2015
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The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method
Bouchard-Côté, A., Vollmer, S. J., and Doucet, A. (2015) · 2015
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Riemann manifold Langevin and Hamiltonian Monte Carlo methods
Girolami, M. and Calderhead, B. (2011) · 2011
Cited alongside, same era.
The theory that would not die: how Bayes’ rule cracked the enigma code, hunted down Russian submarines, & emerged triumphant from two centuries of controversy
McGrayne, S. B. (2011) · 2011
Cited alongside, same era.
MCMC using Hamiltonian dynamics
Neal, R. M. et al. (2011) · 2011
Cited alongside, same era.
A Short History of Markov Chain Monte Carlo: Subjective Recollections from Incomplete Data
Robert, C. and Casella, G. (2011) · 2011
Cited alongside, same era.
Bayesian learning via stochastic gradient Langevin dynamics
Welling, M. and Teh, Y. W. (2011) · 2011
Cited alongside, same era.
Rejection-free Monte Carlo sampling for general potentials
Peters, E. A. J. F. and de With, G. (2012) · 2012
Cited alongside, same era.
On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
Lyne, A.-M., Girolami, M., Atchadé, Y., Strathmann, H., and Simpson, D. (2015) · 2015
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A complete recipe for stochastic gradient MCMC
Ma, Y.-A., Chen, T., and Fox, E. (2015) · 2015
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Speeding up MCMC by efficient data subsampling
Quiroz, M., Villani, M., and Kohn, R. (2015) · 2015
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WASP: Scalable Bayes via barycenters of subset posteriors
Srivastava, S., Cevher, V., Tran-Dinh, Q., and Dunson, D. B. (2015) · 2015
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Piecewise Deterministic Markov Processes for Scalable Monte Carlo on Restricted Domains
Bierkens, J., Bouchard-Cote, A., Duncan, A., Doucet, A., Fearnhead, P., Roberts, G., and Vollmer, S. (2016) · 2016
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Limit theorems for the Zig-Zag process
Bierkens, J. and Duncan, A. (2016) · 2016
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The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data
Bierkens, J., Fearnhead, P., and Roberts, G. (2016) · 2016
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Continuous-time Importance Sampling: Monte Carlo Methods which Avoid Time-Discretisation Error
Fearnhead, P., Latuszynski, K., Roberts, G. O., and Sermaidis, G. (2016) · 2016
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Bayes and Big Data: The Consensus Monte Carlo Algorithm
Scott, S. L., Blocker, A. W., and Bonassi, F. V. (2016) · 2016
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