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There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms.
Equation of state calculations by fast computing machines
Nicholas Metropolis, Arianna W Rosenbluth, Marshall N Rosenbluth, Augusta H Teller, and Edward Teller · 1953
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Some elementary inequalities relating to the gamma and incomplete gamma function
Walter Gautschi · 1959
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Monte carlo calculations of the radial distribution functions for a proton-electron plasma
Av A Barker · 1965
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Monte carlo sampling methods using markov chains and their applications
W Keith Hastings · 1970
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Optimum monte-carlo sampling using markov chains
Peter H Peskun · 1973
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A class of distributions which includes the normal ones
Adelchi Azzalini · 1985
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Hybrid monte carlo
Simon Duane, Anthony D Kennedy, Brian J Pendleton, and Duncan Roweth · 1987
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Exponential convergence of langevin distributions and their discrete approximations
Gareth O Roberts and Richard L Tweedie · 1996
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On some inequalities for the incomplete gamma function
Horst Alzer · 1997
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Weak convergence and optimal scaling of random walk Metropolis algorithms
Gareth O Roberts, Andrew Gelman, and Walter R Gilks · 1997
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Optimal scaling of discrete approximations to Langevin diffusions
Gareth O Roberts and Jeffrey S Rosenthal · 1998
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A note on Metropolis-Hastings kernels for general state spaces
Luke Tierney · 1998
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Geometric ergodicity of Metropolis algorithms
Søren Fiig Jarner and Ernst Hansen · 2000
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Optimal scaling for various Metropolis-Hastings algorithms
Gareth O Roberts and Jeffrey S Rosenthal · 2001
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Slice sampling
Radford M Neal · 2003
Cited alongside, same era.
Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms
Jeffrey S Rosenthal · 2003
Cited alongside, same era.
General state space markov chains and mcmc algorithms
Gareth O Roberts and Jeffrey S Rosenthal · 2004
Cited alongside, same era.
An adaptive version for the metropolis adjusted langevin algorithm with a truncated drift
Yves F Atchade · 2006
Cited alongside, same era.
Statistical mechanics: algorithms and computations , volume 13
Werner Krauth · 2006
Cited alongside, same era.
Coda: Convergence diagnosis and output analysis for mcmc
Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines · 2006
Cited alongside, same era.
The skew-normal and related families
Adelchi Azzalini · 2013
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Optimal tuning of the hybrid monte carlo algorithm
Alexandros Beskos, Natesh Pillai, Gareth Roberts, Jesus-Maria Sanz-Serna, and Andrew Stuart · 2013
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The no-u-turn sampler: adaptively setting path lengths in hamiltonian monte carlo
Matthew D Hoffman and Andrew Gelman · 2014
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Complexity bounds for Markov chain Monte Carlo algorithms via diffusion limits
Gareth O Roberts and Jeffrey S Rosenthal · 2016
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S Dalalyan · 2017
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Nonasymptotic convergence analysis for the unadjusted langevin algorithm
Alain Durmus and Eric Moulines · 2017
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A tutorial on adaptive mcmc
Christophe Andrieu and Johannes Thoms · 2008
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Sufficient conditions for torpid mixing of parallel and simulated tempering
Dawn Woodard, Scott Schmidler, and Mark Huber · 2009
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Exploring an adaptive metropolis algorithm
Benjamin Shaby and Martin T Wells · 2010
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Inverse problems: a bayesian perspective
Andrew M Stuart · 2010
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Handbook of markov chain monte carlo
Steve Brooks, Andrew Gelman, Galin Jones, and Xiao-Li Meng · 2011
Cited alongside, same era.
Mcmc using hamiltonian dynamics
Radford M Neal · 2011
Cited alongside, same era.
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Asymptotic analysis of the random walk metropolis algorithm on ridged densities
Alexandros Beskos, Gareth Roberts, Alexandre Thiery, and Natesh Pillai · 2018
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The tamed unadjusted langevin algorithm
Nicolas Brosse, Alain Durmus, Éric Moulines, and Sotirios Sabanis · 2018
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Piecewise deterministic markov processes for continuous-time monte carlo
Paul Fearnhead, Joris Bierkens, Murray Pollock, Gareth O Roberts, et al · 2018
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On the geometric ergodicity of hamiltonian monte carlo
Samuel Livingstone, Michael Betancourt, Simon Byrne, and Mark Girolami · 2019
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Accelerated sampling on discrete spaces with non-reversible markov processes
Samuel Power and Jacob Vorstrup Goldman · 2019
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Informed proposals for local mcmc in discrete spaces
Giacomo Zanella · 2019
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RStan: the R interface to Stan, 2020
Stan Development Team · 2020
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