M.K. Cowles, G.O. Roberts, and J.S. Rosenthal (December 1997), \Possible biases induced by MCMC convergence diagnostics". Preprint. Home/Search Document Details and Download
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Convergence in the Wasserstein Metric for Markov Chain Monte Carlo .. - Gibbs (1999) (Correct)
....critical issue for users of Markov chain Monte Carlo (MCMC) algorithms is the number of iterations that should be run until the result can be considered a sample from the stationary distribution. Convergence diagnostics do not guarantee convergence, and are known to introduce bias into the results [4]. The theoretical results that exist are difficult to apply in practice. Perfect simulation algorithms [18] 7] are difficult to apply except on discrete state spaces. Recent extensions [17] 8] allow the application of perfect sampling algorithms to uniformly ergodic chains on continuous state ....
Cowles, Mary Kathryn, Roberts, Gareth O., and Rosenthal, Jeffrey S. (1997). Possible biases induced by MCMC convergence diagnostics. To appear in Journal of Statistical Computing and Simulation.
Bounding Convergence Time of the Gibbs Sampler in Bayesian Image.. - Gibbs (1998) (1 citation) (Correct)
.... For a discussion of these issues see, for example, Tierney (1994) and Roberts Rosenthal (1998) Convergence diagnostics (Cowles Carlin (1996) Brooks Roberts (1997) have been developed to monitor convergence of the algorithm while it is running, however none are completely satisfactory (Cowles, Roberts Rosenthal (1997)) There has been much work on developing rigorous, a priori, quantitative bounds on the convergence time (for example, Sinclair Jerrum (1989) Diaconis Stroock (1991) Frieze, Kannon Polson (1994) Ingrassia (1994) Meyn Tweedie (1994) Rosenthal (1995) Mengersen Tweedie (1996) Polson ....
Cowles, M.K., Roberts, G.O. & Rosenthal, J.S. (1997). Possible biases induced by MCMC convergence diagnostics. Preprint.
Parallel computing and Monte Carlo algorithms - Rosenthal (1999) (1 citation) Self-citation (Rosenthal) (Correct)
....work well in practice. However, they have at least two draw backs from the parallel MCMC perspective. First, they sometimes prematurely diagnose convergence by providing a burn in time B which is too small (see e.g. 33] 5] leading to biases as in Subsection 4.1 above. Second, as shown in [6], by basing the burnin time on the sample in progress, convergence diagnostics sometimes introduce biases of their own (even if the Markov chain converges immediately) 13 We thus record: Observation 9. When running parallel Markov chain Monte Carlo, choice of burn in is a very important issue. ....
....this may suggest that the Markov chain has not yet converged, or that there is a problem with the algorithm. This is somewhat related to the multiple runs computer diagnostics of e.g. 18] However, such diagnostic method should be used with care, to avoid introducing additional biases (cf. [6]) In addition, it may be possible to do more sophisticated analysis (e.g. of autocorrelations) on the multiple parallel runs, though this may require greater communication between the di erent computers. 4.3. Theoretical quantitative bounds. It is sometimes possible (cf. 34] 46] 47] to ....
M.K. Cowles, G.O. Roberts, and J.S. Rosenthal (December 1997), \Possible biases induced by MCMC convergence diagnostics". Preprint.
Parallel computing and Monte Carlo algorithms - Rosenthal (1999) (1 citation) Self-citation (Rosenthal) (Correct)
....work well in practice. However, they have at least two draw backs from the parallel MCMC perspective. First, they sometimes prematurely diagnose convergence by providing a burn in time B which is too small (see e.g. 33] 5] leading to biases as in Subsection 4.1 above. Second, as shown in [6], by basing the burnin time on the sample in progress, convergence diagnostics sometimes introduce biases of their own (even if the Markov chain converges immediately) We thus record: Observation 9. When running parallel Markov chain Monte Carlo, choice of burn in is a very important issue. ....
....this may suggest that the Markov chain has not yet converged, or that there is a problem with the algorithm. This is somewhat related to the multiple runs computer diagnostics of e.g. 18] However, such diagnostic method should be used with care, to avoid introducing additional biases (cf. [6]) In addition, it may be possible to do more sophisticated analysis (e.g. of autocorrelations) on the multiple parallel runs, though this may require greater communication between the different computers. 4.3. Theoretical quantitative bounds. It is sometimes possible (cf. 34] 47] 48] to ....
M.K. Cowles, G.O. Roberts, and J.S. Rosenthal (December 1997), "Possible biases induced by MCMC convergence diagnostics". Preprint.
Bounding the convergence time of the Gibbs sampler in Bayesian.. - Gibbs (1998) (1 citation) (Correct)
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Cowles, M.K., Roberts, G.O. & Rosenthal, J.S. (1999). Possible biases induced by MCMC convergence diagnostics. J. Statist. Comp. Simul. 64, 87--104.
Convergence in the Wasserstein Metric for Markov Chain Monte Carlo .. - Gibbs (Correct)
No context found.
Preprint. Cowles, M. K., Roberts, G. O. and Rosenthal, J. S. (1997). Possible biases induced by MCMC convergence diagnostics, Journal of Statistical Computing and Simulation. To appear.
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