The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
General Methods for Monitoring Convergence of Iterative Simulations
Abstract
We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order to develop convergence-monitoring summaries that are relevant for the purposes for which the simulations are used. We recommend applying a battery of tests for mixing based on the comparison of inferences from individual sequences and from the mixture of sequences. Finally, we discuss multivariate analogues, for assessing convergence of several parameters simultaneously.
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“We ran three parallel MCMC chains of 1,000 each after burn-in time of 1,000 iterations, which was sufficient to ensure convergence, as judged by visual inspection of the chain histories and the Gelman–Rubin statistic (Rhat = 1.0 for all parameters in all models; ref. 81).”
From Active learning narrows achievement gaps for underrepresented students in undergraduate science, technology, engineering, and math (2020) · cites this paper as [81]
In the citing paper
“To ensure convergence, trace plots and the BrooksGelmanRubin statistic were assessed.24”
Citations
Cites
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1993) · doi:10.1007/978-1-4899-4541-9 · Cited by 21,230
Inference from iterative simulation using multiple sequences
Gelman, A., & Rubin, D. B. (1992) · Statistical Science · doi:10.1214/ss/1177011136 · Cited by 16,627
Self-citationMarkov Chain Monte Carlo in Practice
Gilks, W. R., Richardson, S. T., & Spiegelhalter, D. J. (1995) · Chapman & Hall/CRC eBooks · doi:10.1201/b14835 · Cited by 7,927
Sampling-based approaches to calculating marginal densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476213 · Cited by 6,606
Fisher, R. A. (1936) · BMJ · doi:10.1136/bmj.1.3923.554-a · Cited by 4,980
The Calculation of Posterior Distributions by Data Augmentation
Tanner, M. A., & Wong, W. H. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478458 · Cited by 3,929
Markov Chains for Exploring Posterior Distributions
Tierney, L. (1994) · The Annals of Statistics · doi:10.1214/aos/1176325750 · Cited by 3,474
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Research works printed but not linked: 3
- Applegate D., 1990, “Random Polynomial Time Algorithms for Sampling from Joint Distributions”
- Gelman A., 1995, Bayesian Statistics 5, 599
- Liu C., Journal of Econometrics
Cited by
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Generalized linear mixed models: a practical guide for ecology and evolution
Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., & White, J.-S. S. (2009) · Trends in Ecology & Evolution · doi:10.1016/j.tree.2008.10.008 · Cited by 8,910
Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach
Smets, F. R., & Wouters, R. (2007) · American Economic Review · doi:10.1257/aer.97.3.586 · Cited by 4,542
Checking consistency in mixed treatment comparison meta-analysis
Dias, S., Welton, N. J., Caldwell, D. M., & Ades, A. E. (2010) · Statistics in Medicine · doi:10.1002/sim.3767 · Cited by 2,521
Nylander, J. A. A., Wilgenbusch, J. C., Warren, D. L., & Swofford, D. L. (2007) · Bioinformatics · doi:10.1093/bioinformatics/btm388 · Cited by 1,751
R2WinBUGS : A Package for Running WinBUGS from R
Sturtz, S., Ligges, U., & Gelman, A. (2005) · Journal of Statistical Software · doi:10.18637/jss.v012.i03 · Cited by 1,654
Self-citation
Metadata
- Authors
- Brooks, S. P., & Gelman, A.
- Affiliations
- University of Bristol (GB)
- Columbia University (US)
- Venue
- Journal of Computational and Graphical Statistics
- Publisher
- Informa UK Limited
- Published
- 1998-12
- Volume
- 7
- Issue
- 4
- Pages
- 434-455
- ISSN
- 1061-8600 (ISSN-L)
- 1537-2715
- OpenAlex
- W2093223772
- Cited by
- 6,045
- References
- 28
- Citations by year
- 2026: 321 · 2025: 371 · 2024: 394 · 2023: 381 · 2022: 341 · 2021: 445 · 2020: 435 · 2019: 370 · 2018: 329 · 2017: 276 · 2016: 305 · 2015: 300 · 2014: 250 · 2013: 244 · 2012: 249
- FWCI
- 15.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Computational and Graphical Statistics (publishedVersion)
- Bristol Research (University of Bristol) (submittedVersion)
- Funders
- National Science Foundation
- KU Leuven
- Engineering and Physical Sciences Research Council
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- convergence monitoring, Markov chain Monte Carlo, mixing test, simulation-based inference
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