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Markov chain Monte Carlo (MCMC) lies at the core of modern Bayesian methodology, much of which would be impossible without it.
Equation of state calculations by fast computing machines
Metropolis, N · 1953
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Markov processes over denumerable products of spaces describing large systems of automata
Wasserstein, L. N · 1969
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Monte Carlo sampling methods using Markov chains and their applications
Hastings, W. K · 1970
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On minimal metrics in the space of random variables
Szulga, A · 1983
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Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
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A class of Wasserstein metrics for probability distributions
Givens, C. R · 1984
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The Monge–Kantorovich mass transference problem and its stochastic applications
Rachev, S. T · 1984
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Bayesian variable selection in linear regression (with discussion)
Mitchell, T. J · 1988
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Bayesian estimation of finite mixture distributions: part ii, Sampling implementation
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Inference from iterative simulation using multiple sequences
Gelman, A · 1992
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Evaluating the accuracy of sampling-based approaches to calculating posterior moments (with discussion)
Geweke, J · 1992
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Variable selection via Gibbs sampling
George, E. I · 1993
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Markov Chains and Stochastic Stability
Meyn, S. P · 1993
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The collapsed Gibbs sampler in Bayesian computations with application to a gene regulation problem
Liu, J. S · 1994
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Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes
Liu, J. S · 1994
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Efficient parametrisations for normal linear mixed models
Gelfand, A. E · 1995
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Markov Chain Monte Carlo in Practice
Gilks, W. R · 1995
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Covariance structure and convergence rate of the Gibbs sampler with various scans
Liu, J. S · 1995
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Minorization conditions and convergence rates for Markov chain Monte Carlo
Rosenthal, J. S · 1995
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Updating schemes, correlation structure, blocking and parametrization for the Gibbs sampler
Roberts, G. O · 1997
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Parameter expansion for data augmentation
Liu, J. S · 1999
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Honest exploration of intractable probability distributions via Markov chain Monte Carlo
Jones, G. L · 2001
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Optimal scaling for various Metropolis–Hastings algorithms
Roberts, G. O · 2001
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Gibbs sampling, conjugate priors, and coupling
Diaconis, P · 2010
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Penalized regression, standard errors, and Bayesian lassos
Kyung, M · 2010
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The Bayesian elastic net
Li, Q · 2010
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Kendall’s Advanced Theory of Statistics, Vol. 2B: Bayesian Statistics
O’Hagan, A · 2010
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Yu, Y · 2011
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Rates of convergence for Gibbs samplers
Hu, V · 2012
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On choosing and bounding probability metrics
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A bivariate beta distribution
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Monte Carlo Strategies in Scientific Computing
Liu, J. S · 2004
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Limitations of Markov chain Monte Carlo algorithms for Bayesian inference of phylogeny
Mossel, E · 2006
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Román, J. C · 2012
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Bayesian inference for logistic models using Polya-Gamma latent variables
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Convergence rate of Markov chain methods for genomic motif discovery
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