The DOI matches its Crossref record; 45 of the 47 references it cites were found in a registry or an index, and 2 are not checked yet.
Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (with Discussion)
Open accessAbstract
Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic Rˆ of Gelman and Rubin (1992) has serious flaws. Traditional Rˆ will fail to correctly diagnose convergence failures when the chain has a heavy tail or when the variance varies across the chains. In this paper we propose an alternative rank-based diagnostic that fixes these problems. We also introduce a collection of quantile-based local efficiency measures, along with a practical approach for computing Monte Carlo error estimates for quantiles. We suggest that common trace plots should be replaced with rank plots from multiple chains. Finally, we give recommendations for how these methods should be used in practice.
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“All of our model estimates met these criteria.”
From The Effects of Generative AI on Design Fixation and Divergent Thinking (2024) · cites this paper as [65]
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“Model inference was performed by Hamiltonian Monte Carlo with the NUTS sampler using PyStan 69 , the Python implementation of Stan.”
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Cites
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003) · doi:10.1201/9780429258480 · Cited by 27,276
Self-citationInference from iterative simulation using multiple sequences
Gelman, A., & Rubin, D. B. (1992) · Statistical Science · doi:10.1214/ss/1177011136 · Cited by 16,627
Self-citationMonte Carlo sampling methods using Markov chains and their applications.
Hastings, W. K. (1970) · Biometrika · doi:10.1093/biomet/57.1.97 · Cited by 15,195
Stan : A Probabilistic Programming Language
Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., & Riddell, A. (2017) · Journal of Statistical Software · doi:10.18637/jss.v076.i01 · Cited by 7,754 · cited 2×
“Adapted from Gelman et al. (2013). packages for MCMC sampling such as Stan (Carpenter et al., 2017), JAGS (Plummer, 2003), WinBUGS (Lunn et al., 2000), OpenBUGS (Lunn et al., 2009), PyMC3 (Salvatier et al., 2016), and NIMBLE (de Valpine et al., 2017), which together are estimated to have hundreds…”
MethodSelf-citationThe use of ranks to avoid the assumption of normality implicit in the analysis of variance
Friedman, M. (1937) · Journal of the American Statistical Association · doi:10.1080/01621459.1937.10503522 · Cited by 7,005
Monte Carlo Statistical Methods
Robert, C., & Casella, G. (2004) · Springer Texts in Statistics · doi:10.1007/978-1-4757-4145-2 · Cited by 5,871
New extension of the Kalman filter to nonlinear systems
Julier, S., & Uhlmann, J. K. (1997) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.280797 · Cited by 5,619
WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility
Lunn, D. J., Thomas, A., Best, N., & Spiegelhalter, D. J. (2000) · Statistics and Computing · doi:10.1023/a:1008929526011 · Cited by 5,397
JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling
Plummer, M. (2003) · Cited by 4,720
CODA: convergence diagnosis and output analysis for MCMC
Plummer, M., Best, N., Cowles, K., & Vines, K. (2006) · Open Research Online (The Open University) · Cited by 3,317
Research works printed but not linked: 3
- Blom, G. (1958). Statistical Estimates and Transformed Beta-Variables. Wiley; New York.
- Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis, third edition. CRC Press. · DOI · Paper page
- Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., and Bürkner, P.-C. (2020). “Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC. Supplementary Material.” Bayesian Analysis. · DOI
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Loomba, S., de Figueiredo, A., Piatek, S. J., de Graaf, K., & Larson, H. J. (2021) · Nature Human Behaviour · doi:10.1038/s41562-021-01056-1 · Cited by 1,800
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Agazie, G., Anumarlapudi, A., Archibald, A. M., Arzoumanian, Z., Baker, P. T., Bécsy, B., Blecha, L., Brazier, A., Brook, P. R., Burke-Spolaor, S., et al. (2023) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/acdac6 · Cited by 1,489
Bayesian statistics and modelling
van de Schoot, R., Depaoli, S. A., King, R., Kramer, B. M. R., Märtens, K., Tadesse, M. G., Vannucci, M., Gelman, A., Veen, D., Willemsen, J. E., et al. (2021) · Nature Reviews Methods Primers · doi:10.1038/s43586-020-00001-2 · Cited by 1,338
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Metadata
- Authors
- Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C.
- Affiliations
- Aalto University (FI)
- Columbia University (US)
- University of Toronto (CA)
- Flatiron Institute (US)
- Venue
- Bayesian Analysis
- Publisher
- Institute of Mathematical Statistics
- Published
- 2021-06-01
- Volume
- 16
- Issue
- 2
- Pages
- 667-718
- ISSN
- 1931-6690 (ISSN-L)
- 1936-0975
- OpenAlex
- W2920804790
- Cited by
- 1,810
- References
- 32
- Citations by year
- 2026: 499 · 2025: 424 · 2024: 328 · 2023: 263 · 2022: 153 · 2021: 93
- FWCI
- 96.56
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by
- Locations
- Bayesian Analysis (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- Aaltodoc (Aalto University) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Data Analysis with R
- Keywords
- convergence diagnostics, Markov chain Monte Carlo, heavy-tailed distributions, Monte Carlo error estimation, trace plots
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