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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Model inference was performed by Hamiltonian Monte Carlo with the NUTS sampler using PyStan 69 , the Python implementation of Stan.”
From Measuring the impact of COVID-19 vaccine misinformation on vaccination intent in the UK and USA (2021) · cites this paper as [71]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
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
Flagged first, then by citations
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
Cited by
Sorted by citations
Items 101–200 of 1,000
Mazzatura, I., Casas, J. R., Salvatore, W., & Caprili, S. (2023) · Engineering Structures · doi:10.1016/j.engstruct.2023.117352 · Cited by 29
Collective incentives reduce over-exploitation of social information in unconstrained human groups
Deffner, D., Mezey, D., Kahl, B., Schakowski, A., Romańczuk, P., Wu, C. M., & Kurvers, R. H. J. M. (2024) · Nature Communications · doi:10.1038/s41467-024-47010-3 · Cited by 29
Johnson, R. M., Stopard, I. J., Byrne, H. M., Armstrong, P. M., Brackney, D. E., & Lambert, B. C. (2024) · PLoS Pathogens · doi:10.1371/journal.ppat.1011975 · Cited by 29
Jacobucci, R., McClure, K. E., & Ammerman, B. A. (2022) · Suicide and Life-Threatening Behavior · doi:10.1111/sltb.12933 · Cited by 29
Zhang, R., Black, R., Sur, D., Karimi, P., Li, K., DeCost, B., Scully, J. R., & Hattrick-Simpers, J. R. (2023) · Journal of The Electrochemical Society · doi:10.1149/1945-7111/aceab2 · Cited by 29
The real-time infection hospitalisation and fatality risk across the COVID-19 pandemic in England
Ward, T., Fyles, M., Glaser, A., Paton, R. S., Ferguson, W., & Overton, C. E. (2024) · Nature Communications · doi:10.1038/s41467-024-47199-3 · Cited by 26
Uncertainty quantification and propagation in surrogate-based Bayesian inference
Reiser, P., Aguilar, J. E., Guthke, A., & Bürkner, P. (2025) · Statistics and Computing · doi:10.1007/s11222-025-10597-8 · Cited by 34
Self-citationGonzales, W. D. W. (2024) · Applied Linguistics · doi:10.1093/applin/amad086 · Cited by 27
Kerioui, M., Mercier, F., Bertrand, J., Tardivon, C., Bruno, R., Guedj, J., & Desmée, S. (2020) · Statistics in Medicine · doi:10.1002/sim.8756 · Cited by 27
A novel framework to predict water turbidity using Bayesian modeling
Huang, J., Qian, R., Gao, J., Bing, H., Qi, L., Qi, L., Song, S., & Huang, J. (2021) · Water Research · doi:10.1016/j.watres.2021.117406 · Cited by 27
Chen, S. M., Bauer, D. J., Belzak, W. C. M., & Brandt, H. (2021) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2021.1948335 · Cited by 29
Bohman, B. J., Culshaw-Maurer, M. J., Abdallah, F. B., Giletto, C. M., Bélanger, G., Fernández, F. G., Miao, Y., MULLA, D. J., & Rosen, C. J. (2023) · European Journal of Agronomy · doi:10.1016/j.eja.2023.126744 · Cited by 26
Adaptive mechanisms of social and asocial learning in immersive collective foraging
Wu, C. M., Deffner, D., Kahl, B., Meder, B., Ho, M. K., & Kurvers, R. H. J. M. (2025) · Nature Communications · doi:10.1038/s41467-025-58365-6 · Cited by 26
Thorp, S., & Mandel, K. S. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac2714 · Cited by 26
Estimating the fitness cost and benefit of antimicrobial resistance from pathogen genomic data
Helekal, D., Keeling, M. J., Grad, Y. H., & Didelot, X. (2023) · Journal of The Royal Society Interface · doi:10.1098/rsif.2023.0074 · Cited by 26
Miller, T. B., Suess, K. A., Setton, D. J., Price, S. H., Labbé, I., Bezanson, R., Brammer, G., Cutler, S. E., Furtak, L. J., Leja, J., et al. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/ade438 · Cited by 25
Freitas, L. P., Schmidt, A. M., Cossich, W., Cruz, O. G., & Carvalho, M. S. (2021) · PLoS neglected tropical diseases · doi:10.1371/journal.pntd.0009537 · Cited by 25
Zitzmann, S., Weirich, S., & Hecht, M. (2021) · Psych · doi:10.3390/psych3030025 · Cited by 26
Huang, W., He, W., Knibbs, L. D., Jalaludin, B. B., Guo, Y., Morawska, L., Heinrich, J., Chen, D.-H., Yu, Y., Zeng, X., et al. (2021) · Environmental Research · doi:10.1016/j.envres.2021.112397 · Cited by 25
Dercon, Q., Mehrhof, S. Z., Sandhu, T., Hitchcock, C., Lawson, R. P., Pizzagalli, D. A., Dalgleish, T., & Nord, C. L. (2023) · Psychological Medicine · doi:10.1017/s0033291723001587 · Cited by 32
TOI-332 b: a super dense Neptune found deep within the Neptunian desert
Osborn, A., Armstrong, D. J., Fernández, J. F., Knierim, H., Adibekyan, V., Collins, K. A., Mena, E. D., Fridlund, M. C., da Silva, J. G., Hellier, C., et al. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad2575 · Cited by 31
Dahirel, M., Bertin, A., Calcagno, V., Duraj, C., Fellous, S., Groussier, G., Lombaert, É., Mailleret, L., Marchand, A., & Vercken, E. (2023) · Peer Community Journal · doi:10.24072/pcjournal.347 · Cited by 24
Gonzales, W. D. W. (2024) · International Journal of Bilingualism · doi:10.1177/13670069231201865 · Cited by 24
Cervantes‐Loreto, A., Ayers, C. A., Dobbs, E. K., Brosi, B. J., & Stouffer, D. B. (2021) · Ecology Letters · doi:10.1111/ele.13765 · Cited by 26
Brans, K. I., Almeida, R. A., & Fajgenblat, M. (2021) · Evolutionary Applications · doi:10.1111/eva.13293 · Cited by 24
Lai, H. R., Chong, K. Y., Yee, A. T. K., Mayfield, M. M., & Stouffer, D. B. (2021) · Ecology · doi:10.1002/ecy.3588 · Cited by 19
Satisfaction with one's job and working at home in the COVID‐19 pandemic: A two‐wave study
Wood, S., Michaelides, G., Inceoglu, I., Niven, K. R., Kelleher, A., Hurren, E. T., & Daniels, K. (2022) · Applied Psychology · doi:10.1111/apps.12440 · Cited by 31
Govic, A., Nasser, H. M., Levay, E. A., Zelko, M. D., Ebrahimie, E., Dehcheshmeh, M. M., Kent, S., Penman, J., & Hazi, A. (2022) · Nutrients · doi:10.3390/nu14214670 · Cited by 24
Simulation-Based Bayesian Analysis
Plummer, M. (2022) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-122121-040905 · Cited by 24
Not All Requirements Prioritization Criteria are Equal at All Times: A Quantitative Analysis
Svensson, R. B., & Torkar, R. (2022) · Journal of Systems and Software · doi:10.1016/j.jss.2023.111909 · Cited by 37
Kumar, A., & Mudgal, A. (2024) · Transportmetrica B Transport Dynamics · doi:10.1080/21680566.2024.2323058 · Cited by 24
Reservoir displacement by an invasive rodent reduces Lassa virus zoonotic spillover risk
Eskew, E. A., Bird, B. H., Ghersi, B. M., Bangura, J. J., Basinski, A. J., Amara, E., Bah, M., Kanu, M. C., Kanu, O. T., Lavalie, E. G., et al. (2024) · Nature Communications · doi:10.1038/s41467-024-47991-1 · Cited by 23
Sweger, S. R., Pribitzer, S., & Stoll, S. (2020) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.0c05026 · Cited by 23
Nudging is Ineffective When Attitudes Are Unsupportive: An Example from a Natural Field Experiment
Dewies, M., Schop-Etman, A., Rohde, K. I. M., & Denktaş, S. (2021) · Basic and Applied Social Psychology · doi:10.1080/01973533.2021.1917412 · Cited by 24
A Bayesian approach to calibrate system dynamics models using Hamiltonian Monte Carlo
Andrade, J., & Duggan, J. (2021) · System Dynamics Review · doi:10.1002/sdr.1693 · Cited by 23
Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy
Bürkner, P., Scholz, M. M., & Radev, S. T. (2023) · Statistics Surveys · doi:10.1214/23-ss145 · Cited by 36
Self-citationP ‐hacking in meta‐analyses: A formalization and new meta‐analytic methods
Mathur, M. B. (2024) · Research Synthesis Methods · doi:10.1002/jrsm.1701 · Cited by 25
Sampaio, J., & Costa, V. A. F. (2021) · Hydrological Sciences Journal · doi:10.1080/02626667.2021.1873997 · Cited by 22
Bayesian model averaging for mortality forecasting using leave-future-out validation
Barigou, K., Goffard, P.-O., Loisel, S., & Salhi, Y. (2022) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2022.01.011 · Cited by 22
Svensson, I., Ekström, A., & Forssén, C. (2022) · Physical Review C · doi:10.1103/physrevc.105.014004 · Cited by 22
Kajihara, K. T., Egan, C., Swift, S. O. I., Wall, C. B., Muir, C. D., & Hynson, N. A. (2022) · New Phytologist · doi:10.1111/nph.18058 · Cited by 23
Zheng, Z., Weinberger, D. M., & Pitzer, V. E. (2022) · npj Vaccines · doi:10.1038/s41541-022-00550-5 · Cited by 22
Cortical speech tracking is related to individual prediction tendencies
Schubert, J., Schmidt, F., Gehmacher, Q., Bresgen, A., & Weisz, N. (2023) · Cerebral Cortex · doi:10.1093/cercor/bhac528 · Cited by 22
Keddie, S., Baerenbold, O., Keogh, R. H., & Bradley, J. (2023) · BMC Medical Research Methodology · doi:10.1186/s12874-023-01873-0 · Cited by 22
Fajardo, A., Siefert, A., & Laughlin, D. C. (2023) · Journal of Ecology · doi:10.1111/1365-2745.14240 · Cited by 25
Thiele, L., Marques, G. A., Liu, J., & Shirasaki, M. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.123526 · Cited by 21
Horseshoe prior Bayesian quantile regression
Kohns, D., & Szendrei, T. (2023) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1093/jrsssc/qlad091 · Cited by 21
South, L. F., Riabiz, M., Teymur, O., & Oates, C. J. (2021) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-040220-091727 · Cited by 21
Flexible and efficient Bayesian pharmacometrics modeling using Stan and Torsten, Part I
Margossian, C. C., Zhang, Y., & Gillespie, W. R. (2022) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.12812 · Cited by 20
Gilman, E. L., Chaloupka, M. Y., Benaka, L. R., Bowlby, H. D., Fitchett, M., Kaiser, M. J., & Musyl, M. K. (2022) · Scientific Reports · doi:10.1038/s41598-022-21976-w · Cited by 20
Strack, T., Schmidt, D., & Stoll, M. (2021) · Agricultural and Forest Meteorology · doi:10.1016/j.agrformet.2021.108515 · Cited by 21
Rognli, E. W., Zahl‐Olsen, R., Rekdal, S. S., Hoffart, A., & Bertelsen, T. B. (2022) · Journal of Child Psychology and Psychiatry · doi:10.1111/jcpp.13662 · Cited by 21
Ontogeny shapes individual dietary specialization in female European brown bears (Ursus arctos)
Hertel, A. G., Albrecht, J., Selva, N., Sergiel, A., Hobson, K. A., Janz, D. M., Mulch, A., Kindberg, J., Hansen, J., Frank, S. C., et al. (2024) · Nature Communications · doi:10.1038/s41467-024-54722-z · Cited by 20
Spectral physical unclonable functions: downscaling randomness with multi-resonant hybrid particles
Sandomirskii, M., Petrova, E. A., Kustov, P., Chizhov, L., Larin, A. O., Bruyère, S., Yaroshenko, V. V., Игоревич, А. Э., Belov, P. A., & Zuev, D. A. (2025) · Nature Communications · doi:10.1038/s41467-025-60121-9 · Cited by 33
Zero and One Inflated Item Response Theory Models for Bounded Continuous Data
Molenaar, D., Cúri, M., & Bazán, J. L. (2022) · Journal of Educational and Behavioral Statistics · doi:10.3102/10769986221108455 · Cited by 20
Spatial scale selection for informing species conservation in a changing landscape
Monroe, A. P., Heinrichs, J. A., Whipple, A. L., O’Donnell, M. S., Edmunds, D. R., & Aldridge, C. L. (2022) · Ecosphere · doi:10.1002/ecs2.4320 · Cited by 20
Terrestrial invasive species alter marine vertebrate behaviour
Gunn, R. L., Benkwitt, C. E., Graham, N. A. J., Hartley, I. R., Algar, A. C., & Keith, S. A. (2023) · Nature Ecology & Evolution · doi:10.1038/s41559-022-01931-8 · Cited by 21
Price Prediction of Bitcoin Based on Adaptive Feature Selection and Model Optimization
Zhu, Y., Ma, J., Gu, F., Wang, J., Li, Z., Zhang, Y., Xu, J., Li, Y., Wang, Y., & Yang, X. (2023) · Mathematics · doi:10.3390/math11061335 · Cited by 20
Investigating the turbulent hot gas in X-COP galaxy clusters
Dupourqué, S., Clerc, N., Pointecouteau, É., Eckert, D., Ettori, S., & Vazza, F. (2023) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202245779 · Cited by 20
Glyphosate impairs aversive learning in bumblebees
Nouvian, M., Foster, J. J., & Weidenmüller, A. (2023) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2023.165527 · Cited by 20
dockerHDDM: A user-friendly environment for Bayesian Hierarchical Drift-Diffusion ModelingPreprint
Pan, W., Geng, H., Zhang, L., Fengler, A., Frank, M. J., Zhang, R., & Chuan-Peng, H. (2022) · doi:10.31234/osf.io/6uzga · Cited by 20
How Occam’s razor guides human decision-makingPreprint
Piasini, E., Liu, S., Chaudhari, P., Balasubramanian, V., & Gold, J. I. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.01.10.523479 · Cited by 20
Correcting Misclassification Errors in Crowdsourced Ecological Data: A Bayesian Perspective
Santos–Fernández, E., Peterson, E. E., Vercelloni, J., Rushworth, E., & Mengersen, K. L. (2020) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12453 · Cited by 19
Wohlfahrt, Y., Patz, C., Schmidt, D., Rauhut, D., Honermeier, B., & Stoll, M. (2021) · Foods · doi:10.3390/foods10010145 · Cited by 19
Disentangling Multiple Stochastic Gravitational Wave Background Sources in PTA Data Sets
Kaiser, A. R., Pol, N. S., McLaughlin, M. A., Chen, S., Hazboun, J. S., Kelley, L. Z., Simon, J., Taylor, S. R., Vigeland, S. J., & Witt, C. A. (2022) · The Astrophysical Journal · doi:10.3847/1538-4357/ac86cc · Cited by 19
Impact of the Euro 2020 championship on the spread of COVID-19
Dehning, J., Mohr, S., Contreras, S., Dönges, P., Iftekhar, E. N., Schulz, O., Bechtle, P., & Priesemann, V. (2023) · Nature Communications · doi:10.1038/s41467-022-35512-x · Cited by 18
Illustrating the Value of Prior Predictive Checking for Bayesian Structural Equation Modeling
Winter, S. D., & Depaoli, S. A. (2023) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2022.2164286 · Cited by 24
A Primer on Bayesian Neural Networks: Review and Debates
Arbel, J., Pitas, K., Vladimirova, M., & Fortuin, V. (2026) · Statistical Science · doi:10.1214/24-sts969 · Cited by 78
A Statistical Perspective on the Challenges in Molecular Microbial Biology
Jeganathan, P., & Holmes, S. (2021) · Journal of Agricultural Biological and Environmental Statistics · doi:10.1007/s13253-021-00447-1 · Cited by 20
A practical guide to pseudo-marginal methods for computational inference in systems biology
Warne, D. J., Baker, R. E., & Simpson, M. J. (2020) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2020.110255 · Cited by 19
Trait‐matching models predict pairwise interactions across regions, not food web properties
Caron, D., Brose, U., Lurgi, M., Blanchet, F. G., Gravel, D., & Pollock, L. J. (2024) · Global Ecology and Biogeography · doi:10.1111/geb.13807 · Cited by 18
Estimating causal effects from panel data with dynamic multivariate panel models
Helske, J., & Tikka, S. (2024) · Advances in Life Course Research · doi:10.1016/j.alcr.2024.100617 · Cited by 23
South, L. F., Riabiz, M., Teymur, O., & Oates, C. J. (2021) · Research Portal (King's College London) · Cited by 18
Gabriel, S., Ncube, M., Zeiler, E., Thompson, N., Karlsen, M. C., Goldman, D., Glavas, Z., Beauchesne, A. R., Scharf, E. L., Goldhamer, A. C., et al. (2022) · Nutrients · doi:10.3390/nu14204313 · Cited by 18
Rmus, M., He, M., Baribault, B., Walsh, E. G., Festa, E. K., Collins, A. G. E., & Nassar, M. R. (2023) · eLife · doi:10.7554/elife.85243 · Cited by 25
Bürkner, P., Kröker, I., Oladyshkin, S., & Nowak, W. (2023) · Journal of Computational Physics · doi:10.1016/j.jcp.2023.112210 · Cited by 18
Self-citationGoetsch, C., Gulka, J. E., Friedland, K. D., Winship, A. J., Clerc, J., Gilbert, A., Goyert, H. F., Stenhouse, I. J., Williams, K. A., Willmott, J. R., et al. (2023) · Ecology and Evolution · doi:10.1002/ece3.10226 · Cited by 19
Storm surge hazard estimation along the US Gulf Coast: A Bayesian hierarchical approach
Boumis, G., Moftakhari, H. R., & Moradkhani, H. (2023) · Coastal Engineering · doi:10.1016/j.coastaleng.2023.104371 · Cited by 17
Mapping cognitive processes in video-based learning by combining trace and think-aloud data
Gijsen, M., Catrysse, L., Mæyer, S. D., & Gijbels, D. (2023) · Learning and Instruction · doi:10.1016/j.learninstruc.2023.101851 · Cited by 26
Inferring fungal growth rates from optical density data
Hameed, T., Motsi, N., Bignell, E., & Tanaka, R. J. (2024) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1012105 · Cited by 19
Bayesian approach to longitudinal craniofacial growth: The Craniofacial Growth Consortium Study
Sherwood, R. J., Oh, H. S., Valiathan, M., McNulty, K. P., Duren, D. L., Knigge, R. P., Hardin, A. M., Holzhauser, C. L., & Middleton, K. M. (2020) · The Anatomical Record · doi:10.1002/ar.24520 · Cited by 21
Lai, M. H. C., Liu, Y., & Tse, W. W.-Y. (2021) · Behavior Research Methods · doi:10.3758/s13428-021-01560-2 · Cited by 18
Eyster, H. N., & Beckage, B. (2022) · Atmosphere · doi:10.3390/atmos13050830 · Cited by 18
Temperature synchronizes temporal variation in laying dates across European hole‐nesting passerines
Vriend, S. J. G., Grøtan, V., Gamelon, M., Adriaensen, F., Ahola, M., Álvarez, E., Bailey, L. D., Barba, E., Bouvier, J., Burgess, M. D., et al. (2022) · Ecology · doi:10.1002/ecy.3908 · Cited by 18
Uncertainty in Bayesian Leave-One-Out Cross-Validation Based Model Comparison
Sivula, T., Magnusson, M., Matamoros, A. A., & Vehtari, A. (2025) · Bayesian Analysis · doi:10.1214/25-ba1569 · Cited by 199
Self-citationFricke, L., Destruel, É., Zimmermann, M., & Onea, E. (2023) · Frontiers in Psychology · doi:10.3389/fpsyg.2023.1148275 · Cited by 18
Brown, H. A., Topham, T. H., Clark, B., Ioannou, L. G., Flouris, A. D., Smallcombe, J. W., Telford, R. D., Jay, O., & Périard, J. D. (2023) · Sports Medicine · doi:10.1007/s40279-023-01972-4 · Cited by 17
Post-Eccentric Flywheel Underwater Undulatory Swimming Potentiation in Competitive Swimmers
Crespo, E., Ruiz-Navarro, J. J., Cuenca‐Fernández, F., & Arellano, R. (2021) · Journal of Human Kinetics · doi:10.2478/hukin-2021-0068 · Cited by 17
Mease, P. J., McInnes, I. B., Tam, L., Rajalingam, R., Peterson, S., Hassan, F., Chakravarty, S. D., Contré, C., Armstrong, A., Boehncke, W., et al. (2022) · Rheumatology · doi:10.1093/rheumatology/keac500 · Cited by 18
Deducing subnanometer cluster size and shape distributions of heterogeneous supported catalysts
Liao, V., Cohen, M., Wang, Y., & Vlachos, D. G. (2023) · Nature Communications · doi:10.1038/s41467-023-37664-w · Cited by 17
Bahramian, A., Tremou, E., Tetarenko, A. J., Miller-Jones, J. C. A., Fender, R. P., Corbel, S., Williams, D. R., Strader, J., Carotenuto, F., Salinas, R., et al. (2023) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/accde1 · Cited by 17
Guy, H., Vittoz, S., Caputo, G., & Thiery, T. (2023) · Energy and Buildings · doi:10.1016/j.enbuild.2023.113595 · Cited by 17
Yarrow, K., Solomon, J. A., Arnold, D. H., & Roseboom, W. (2023) · Journal of Experimental Psychology Human Perception & Performance · doi:10.1037/xhp0001154 · Cited by 17
On the hierarchical Bayesian modelling of frequency response functions
DARDENO, T. A., Keith Worden, B., Dervilis, N., Mills, R. S., & Bull, L. A. (2024) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2023.111072 · Cited by 17
Robust, Accurate Stochastic Optimization for Variational Inference
Dhaka, A. K., Catalina, A., Andersen, M. R., Magnusson, M., Huggins, J. H., & Vehtari, A. (2020) · OpenBU (Boston University) · doi:10.48550/arxiv.2009.00666 · Cited by 17
Self-citationLisi, M. P., Fusaro, M., Tieri, G., & Aglioti, S. M. (2021) · Computers in Human Behavior · doi:10.1016/j.chb.2021.106948 · Cited by 17
Magee, A. F., & Höhna, S. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.01.14.426715 · Cited by 17
A Continuous Root Water Uptake Isotope Mixing Model
Fu, H., Neil, E. J., Liu, J., & Si, B. (2024) · Water Resources Research · doi:10.1029/2023wr036852 · Cited by 16
The influence of age and experience of (un)fairness on third‐party punishment in children
Lee, Y.-E., & Warneken, F. (2022) · Social Development · doi:10.1111/sode.12604 · Cited by 17
Topological models to infer multiphase interstellar medium properties
Lebouteiller, V., & Ramambason, L. (2022) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202243865 · Cited by 16
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review