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Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity.
Monte Carlo sampling methods using Markov chains and their applications
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The existence of moments for stationary Markov chains
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Econometric issues in the analysis of regressions with generated regressors
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Hybrid Monte Carlo
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Nonuniversal critical dynamics in Monte Carlo simulations
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Comparison between cluster Monte Carlo algorithms in the Ising model
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Markov chain Monte Carlo maximum likelihood
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Analysis of parallel replicated simulations under a completion time constraint
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The asymptotic efficiency of simulation estimators
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Bayesian learning via stochastic dynamics
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Regeneration in Markov chain samplers
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General strategies for assessing convergence of MCMC algorithms using coupled sample paths
A. Reutter and V. E. Johnson · 1995
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Studying convergence of Markov chain Monte Carlo algorithms using coupled sample paths
V. E. Johnson · 1996
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Exact sampling with coupled Markov chains and applications to statistical mechanics
J. G. Propp and D. B. Wilson · 1996
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Analysis of the Gibbs sampler for a model related to James-Stein estimators
J. S. Rosenthal · 1996
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Regression shrinkage and selection via the Lasso
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Weak convergence and optimal scaling of random walk Metropolis algorithms
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Faithful couplings of Markov chains: now equals forever
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A simulation approach to convergence rates for Markov chain Monte Carlo algorithms
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A coupling-regeneration scheme for diagnosing convergence in Markov chain Monte Carlo algorithms
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Exact sampling from a continuous state space
D. J. Murdoch and P. J. Green · 1998
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Iterated random functions
P. Diaconis and D. Freedman · 1999
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Circularly-coupled Markov chain sampling
R. M. Neal · 1999
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Geometric ergodicity of metropolis algorithms
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Parallel computing and Monte Carlo algorithms
J. S. Rosenthal · 2000
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Coupling, stationarity, and regeneration , volume 14
H. Thorisson · 2000
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Neural network credit scoring models
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Explaining the perfect sampler
G. Casella, M. Lavine, and C. P. Robert · 2001
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Improving Markov chain Monte Carlo estimators by coupling to an approximating chain
R. M. Neal and R. L. Pinto · 2001
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Lectures on the coupling method
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Estimation and inference in two-step econometric models
K. M. Murphy and R. H. Topel · 2002
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MC’s for MCMC’ists
E. Nummelin · 2002
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Quantitative convergence rates of Markov chains: A simple account
J. S. Rosenthal · 2002
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JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling
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Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference
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Quantitative bounds on convergence of time-inhomogeneous markoc chains
R. Douc, E. Moulines, and J. S. Rosenthal · 2004
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Least angle regression
B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani · 2004
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Monte Carlo statistical methods
C. P. Robert and G. Casella · 2004
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General state space Markov chains and MCMC algorithms
G. O. Roberts and J. S. Rosenthal · 2004
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Using all Metropolis–Hastings proposals to estimate mean values
H. Tjelmeland · 2004
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Identification of regeneration times in mcmc simulation, with application to adaptive schemes
A. E. Brockwell and J. B. Kadane · 2005
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The No-U-Turn Sampler: adaptively setting path lengths in Hamiltonian Monte Carlo
M. D. Hoffman and A. Gelman · 2014
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Perfect simulation using atomic regeneration with application to sequential Monte Carlo
A. Lee, A. Doucet, and K. Łatuszyński · 2014
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Geometric ergodicity for Bayesian shrinkage models
S. Pal and K. Khare · 2014
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Cuts in Bayesian graphical models
M. Plummer · 2014
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Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms
C. Andrieu and M. Vihola · 2015
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On risk bounds in isotonic and other shape restricted regression problems
S. Chatterjee, A. Guntuboyina, B. Sen, et al · 2015
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An adaptive version for the Metropolis adjusted Langevin algorithm with a truncated drift
Y. F. Atchade · 2006
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Parallel Markov chain Monte Carlo simulation by pre-fetching
A. E. Brockwell · 2006
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CODA: convergence diagnosis and output analysis for MCMC
M. Plummer, N. Best, K. Cowles, and K. Vines · 2006
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Credit scoring with a data mining approach based on support vector machines
C.-L. Huang, M.-C. Chen, and C.-J. Wang · 2007
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Markov chain Monte Carlo: can we trust the third significant figure?
J. M. Flegal, M. Haran, and G. L. Jones · 2008
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Monte Carlo strategies in scientific computing
J. S. Liu · 2008
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A practical sequential stopping rule for high-dimensional Markov chain Monte Carlo
L. Gong and J. M. Flegal · 2015
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Bayesian computation: a summary of the current state, and samples backwards and forwards
P. J. Green, K. Łatuszyński, M. Pereyra, and C. P. Robert · 2015
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R: A Language and Environment for Statistical Computing
R Core Team · 2015
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WASP: Scalable Bayes via barycenters of subset posteriors
S. Srivastava, V. Cevher, Q. Dinh, and D. Dunson · 2015
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Parallelizing MCMC with random partition trees
X. Wang, F. Guo, K. A. Heller, and D. B. Dunson · 2015
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Markov chain Monte Carlo confidence intervals
Y. F. Atchadé · 2016
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Exact simulation versus exact estimation
P. W. Glynn · 2016
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Perfect simulation , volume 148
M. Huber · 2016
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Bayesian variable selection for binary outcomes in high-dimensional genomic studies using non-local priors
A. Nikooienejad, W. Wang, and V. E. Johnson · 2016
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The scalable Langevin exact algorithm: Bayesian inference for big data
M. Pollock, P. Fearnhead, A. M. Johansen, and G. O. Roberts · 2016
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On the computational complexity of high-dimensional Bayesian variable selection
Y. Yang, M. J. Wainwright, and M. I. Jordan · 2016
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The central role of Bayes theorem for joint estimation of causal effects and propensity scores
C. M. Zigler · 2016
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Massively parallel MCMC for Bayesian hierarchical models
R. J. Goudie, R. M. Turner, D. De Angelis, and A. Thomas · 2017
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Better together? Statistical learning in models made of modules
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Coupling and decoupling to bound an approximating Markov chain
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Rapid mixing of Hamiltonian Monte Carlo on strongly log-concave distributions
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Statistically efficient thinning of a Markov chain sampler
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Asymptotic bias of stochastic gradient search
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The Hamming ball sampler
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Piecewise deterministic Markov chain Monte Carlo
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Unbiased estimators and multilevel Monte Carlo
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On parallelizable Markov chain Monte Carlo algorithms with waste-recycling
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Geometric integrators and the Hamiltonian Monte Carlo method
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Coupling and convergence for Hamiltonian Monte Carlo
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