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Gelman and Rubin's (1992) convergence diagnostic is one of the most popular methods for terminating a Markov chain Monte Carlo (MCMC) sampler.
Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo
Vats, D., Flegal, J. M., and Jones, G. L. (2018) · 1909
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Certain generalizations in the analysis of variance
Wilks, S. S. (1932) · 1932
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Multivariate estimation in regenerative simulation
Seila, A. F. (1982) · 1982
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Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions
SenGupta, A. (1987) · 1987
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Inference from iterative simulation using multiple sequences (with discussion)
Gelman, A. and Rubin, D. B. (1992) · 1992
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Minorization conditions and convergence rates for Markov chain Monte Carlo
Rosenthal, J. S. (1995) · 1995
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Markov chain Monte Carlo convergence diagnostics: A comparative review
Cowles, M. K. and Carlin, B. P. (1996) · 1996
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Weak convergence and optimal scaling of random walk Metropolis algorithms
Roberts, G. O., Gelman, A., Gilks, W. R., et al. (1997) · 1997
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General methods for monitoring convergence of iterative simulations
Brooks, S. P. and Gelman, A. (1998) · 1998
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Markov chain Monte Carlo in practice: a roundtable discussion
Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. M. (1998) · 1998
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Monte Carlo error estimation for multivariate Markov chains
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Honest exploration of intractable probability distributions via Markov chain Monte Carlo
Jones, G. L. and Hobert, J. P. (2001) · 2001
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Replicated batch means for steady-state simulations
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Relative fixed-width stopping rules for Markov chain Monte Carlo simulations
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A practical sequential stopping rule for high-dimensional Markov chain Monte Carlo
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Multivariate initial sequence estimators in Markov chain Monte Carlo
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MCMC diagnostics for higher dimensions using Kullback Leibler divergence
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Monitoring joint convergence of MCMC samplers
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Weighted batch means estimators in Markov chain Monte Carlo
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