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.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
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?
MCMC chains were sufficient to ensure convergence, as judged by visual inspection and the Gelman-Rubin statistic (Rhat = 1.0).
“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]
Convergence was checked with trace plots and the Brooks-Gelman-Rubin statistic.
“To ensure convergence, trace plots and the BrooksGelmanRubin statistic were assessed.24”
Cites
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500 · see citing works
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1993) · doi:10.1007/978-1-4899-4541-9 · Cited by 21,230 · see citing works
Inference from iterative simulation using multiple sequences
Gelman, A., & Rubin, D. B. (1992) · Statistical Science · doi:10.1214/ss/1177011136 · Cited by 16,627 · see citing works
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 · see citing works
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 · see citing works
Fisher, R. A. (1936) · BMJ · doi:10.1136/bmj.1.3923.554-a · Cited by 4,980 · see citing works
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 · see citing works
Markov Chains for Exploring Posterior Distributions
Tierney, L. (1994) · The Annals of Statistics · doi:10.1214/aos/1176325750 · Cited by 3,513 · see citing works
Journal of the Royal Statistical Society.
(1923) · The Economic Journal · doi:10.1093/ej/33.130.269 · Cited by 3,289 · see citing works
Bayes and Empirical Bayes Methods for Data Analysis
Carlin, B. P., & Louis, T. A. (2001) · Technometrics · doi:10.1198/tech.2001.s608 · Cited by 2,110 · see citing works
Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
Cowles, M. K., & Carlin, B. P. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476956 · Cited by 1,998 · see citing works
Markov Chain Monte Carlo in Practice
Gasparini, M., Gilks, W. R., Richardson, S. T., & Spiegelhalter, D. J. (1997) · Technometrics · doi:10.2307/1271145 · Cited by 1,881 · see citing works
Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods
Smith, A. F. M., & Roberts, G. O. (1993) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1993.tb01466.x · Cited by 1,713 · see citing works
Smith, J. Q., Bernardo, J. M., Berger, J. O., Dawid, A. P., & Smith, A. F. M. (1993) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.2307/2982740 · Cited by 1,098 · see citing works
Bayesian Computation and Stochastic Systems
Besag, J. E., Green, P., Higdon, D., & Mengersen, K. L. (1995) · Statistical Science · doi:10.1214/ss/1177010123 · Cited by 943 · see citing works
Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
Rosenthal, J. S. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476548 · Cited by 480 · see citing works
Bayes and Empirical Bayes Methods for Data Analysis
Rukhin, A. L., Carlin, B. P., & Louis, T. A. (1997) · Technometrics · doi:10.2307/1271144 · Cited by 454 · see citing works
Physiological Pharmacokinetic Analysis Using Population Modeling and Informative Prior Distributions
Gelman, A., Bois, F., & Jiang, J. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476708 · Cited by 353 · see citing works
Self-citationEfficient parametrisations for normal linear mixed models
Gelfand, A. E., Sahu, S. K., & Carlin, B. P. (1995) · Biometrika · doi:10.1093/biomet/82.3.479 · Cited by 306 · see citing works
Bayesian Inference for Generalized Linear and Proportional Hazards Models via Gibbs Sampling
Δελλαπόρτας, Π., & Smith, A. F. M. (1993) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.2307/2986324 · Cited by 250 · see citing works
[Bayesian Computation and Stochastic Systems]: Rejoinder
Besag, J. E., Green, P., Higdon, D., & Mengersen, K. L. (1995) · Statistical Science · doi:10.1214/ss/1177010130 · Cited by 220 · see citing works
A Single Series from the Gibbs Sampler Provides a False Sense of Security
Gelman, A., & Rubin, D. B. (1992) · doi:10.1093/oso/9780198522669.003.0038 · Cited by 204 · see citing works
Self-citationStationarity detection in the initial transient problem
Asmussen, S., Glynn, P. W., & Þórisson, H. (1992) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/137926.137932 · Cited by 120 · see citing works
(2013) · Statistics and Computing · doi:10.1007/11222.1573-1375 · Cited by 116 · see citing works
Backhaus, K., Erichson, B., Gensler, S., Weiber, R., & Weiber, T. (2023) · Springer eBooks · doi:10.1007/978-3-658-40411-6 · Cited by 100 · see citing works
Bayesian Estimation for the Three-Parameter Weibull Distribution with Tree Diameter Data
Green, E. J., Roesch, F. A., Smith, A. F. M., & Strawderman, W. E. (1994) · Biometrics · doi:10.2307/2533217 · Cited by 50 · see citing works
Applications of Bayesian Software: Two Examples
Grieve, A. P. (1987) · Journal of the Royal Statistical Society Series D (The Statistician) · doi:10.2307/2348525 · Cited by 26 · see citing works
Markov-Normal analysis of iterative simulations before their convergence
Liu, C., & Rubin, D. B. (1996) · Journal of Econometrics · doi:10.1016/0304-4076(95)01769-0 · Cited by 17 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
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 · see citing works
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 · see citing works
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 · see citing works
Nylander, J. A. A., Wilgenbusch, J. C., Warren, D. L., & Swofford, D. L. (2007) · Bioinformatics · doi:10.1093/bioinformatics/btm388 · Cited by 1,751 · see citing works
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 1,566 · see citing works
Self-citationA century of trends in adult human height
NCD Risk Factor Collaboration (NCD-RisC) (2016) · eLife · doi:10.7554/elife.13410 · Cited by 1,558 · see citing works
Shocks and Frictions in US Business Cycles: A Bayesian DSGE ApproachPreprint
Smets, F. R., & Wouters, R. (2010) · SSRN Electronic Journal · doi:10.2139/ssrn.1687574 · Cited by 1,518 · see citing works
Theobald, E. J., Hill, M. J., Tran, E., Agrawal, S., Arroyo, E. N., Behling, S., Chambwe, N., Cintrón, D. L., Cooper, J. D., Dunster, G., et al. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1916903117 · Cited by 1,387 · see citing works
(2013) · Cited by 1,351 · see citing works
Credit and banking in a DSGE model of the euro areaPreprint
Gerali, A., Neri, S., Sessa, L., & Signoretti, F. M. (2010) · RePEc: Research Papers in Economics · doi:10.1111/j.1538-4616.2010.00331.x · Cited by 1 · see citing works
Pharmacological interventions for smoking cessation: an overview and network meta-analysis
Cahill, K., Stevens, S., Perera, R., & Lancaster, T. (2013) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd009329.pub2 · Cited by 1,243 · see citing works
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 1,185 · see citing works
Self-citationWhite, I. R., Barrett, J. K., Jackson, D., & Higgins, J. P. T. (2012) · Research Synthesis Methods · doi:10.1002/jrsm.1045 · Cited by 1,114 · see citing works
Bayesian stable isotope mixing models
Parnell, A. C., Phillips, D. L., Bearhop, S., Semmens, B. X., Ward, E. J., Moore, J. W., Jackson, A. L., Grey, J., Kelly, D. J. A., & Inger, R. (2013) · Environmetrics · doi:10.1002/env.2221 · Cited by 1,099 · see citing works
Vrugt, J. A. (2015) · Environmental Modelling & Software · doi:10.1016/j.envsoft.2015.08.013 · Cited by 856 · see citing works
The Time-Varying Volatility of Macroeconomic Fluctuations
Justiniano, A., & Primiceri, G. E. (2008) · American Economic Review · doi:10.1257/aer.98.3.604 · Cited by 844 · see citing works
EXTRACTING MORE OUT OF RELOCATION DATA: BUILDING MOVEMENT MODELS AS MIXTURES OF RANDOM WALKS
Morales, J. M., Haydon, D. T., Frair, J. L., Holsinger, K. E., & Fryxell, J. M. (2004) · Ecology · doi:10.1890/03-0269 · Cited by 801 · see citing works
Automating network meta‐analysis
van Valkenhoef, G., Lu, G., de Brock, B., Hillege, H. L., Ades, A. E., & Welton, N. J. (2012) · Research Synthesis Methods · doi:10.1002/jrsm.1054 · Cited by 793 · see citing works
Theobald, E. J., Ettinger, A., Burgess, H., Debey, L. B., Schmidt, N., Froehlich, H., Wagner, C., HilleRisLambers, J., Tewksbury, J., Harsch, M., et al. (2015) · Biological Conservation · doi:10.1016/j.biocon.2014.10.021 · Cited by 710 · see citing works
Mccarthy, M. A. (2007) · Cambridge University Press eBooks · doi:10.1017/cbo9780511802454 · Cited by 758 · see citing works
Cipriani, A., Zhou, X., Del Giovane, C., Hetrick, S. E., Qin, B., Whittington, C., Coghill, D., Zhang, Y., Hazell, P., Leucht, S., et al. (2016) · The Lancet · doi:10.1016/s0140-6736(16)30385-3 · Cited by 734 · see citing works
Climate change contributes to widespread declines among bumble bees across continents
Soroye, P., Newbold, T., & Kerr, J. T. (2020) · Science · doi:10.1126/science.aax8591 · Cited by 720 · see citing works
boa : An R Package for MCMC Output Convergence Assessment and Posterior Inference
Smith, B. J. (2007) · Journal of Statistical Software · doi:10.18637/jss.v021.i11 · Cited by 705 · see citing works
The Incubation Periods of Dengue Viruses
Chan, M., & Johansson, M. A. (2012) · PLoS ONE · doi:10.1371/journal.pone.0050972 · Cited by 677 · see citing works
Yuan, Y., & MacKinnon, D. P. (2009) · Psychological Methods · doi:10.1037/a0016972 · Cited by 641 · see citing works
Gordon, B. A., Blazey, T. M., Su, Y., Hari-Raj, A., Dincer, A., Flores, S., Christensen, J., McDade, E., Wang, G., Xiong, C., et al. (2018) · The Lancet Neurology · doi:10.1016/s1474-4422(18)30028-0 · Cited by 602 · see citing works
Wandel, S., Jüni, P., Tendal, B., Nüesch, E., Villiger, P. M., Welton, N. J., Reichenbach, S., & Trelle, S. (2010) · BMJ · doi:10.1136/bmj.c4675 · Cited by 577 · see citing works
Efficient sampling of fast and slow cosmological parameters
Lewis, A. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.103529 · Cited by 576 · see citing works
Estimating Snow Water Equivalent Using Snow Depth Data and Climate Classes
Sturm, M., Taras, B. D., Liston, G. E., Derksen, C., Jonas, T., & Lea, J. T. (2010) · Journal of Hydrometeorology · doi:10.1175/2010jhm1202.1 · Cited by 572 · see citing works
Barth, J., Munder, T., Gerger, H., Nüesch, E., Trelle, S., Znoj, H., Jüni, P., & Cuijpers, P. (2013) · PLoS Medicine · doi:10.1371/journal.pmed.1001454 · Cited by 569 · see citing works
Xu, C., Chen, Y., Du, X.-J., Liu, J.-Q., Huang, C.-L., Chen, L., Zhou, G., Li, W., Mao, Y., Hsu, C., et al. (2018) · BMJ · doi:10.1136/bmj.k4226 · Cited by 560 · see citing works
Post-operative mortality, missed care and nurse staffing in nine countries: A cross-sectional study
Ball, J., Bruyneel, L., Aiken, L. H., Sermeus, W., Sloane, D. M., Rafferty, A. M., Lindqvist, R., Tishelman, C., & Griffiths, P. (2017) · International Journal of Nursing Studies · doi:10.1016/j.ijnurstu.2017.08.004 · Cited by 545 · see citing works
Orenstein, E. W., Basu, S., Shah, N. S., Andrews, J. R., Friedland, G. H., Moll, A. P., Gandhi, N. R., & Galvani, A. P. (2009) · The Lancet Infectious Diseases · doi:10.1016/s1473-3099(09)70041-6 · Cited by 540 · see citing works
Comparative studies of quantitative trait and neutral marker divergence: a meta‐analysis
Leinonen, T., O’Hara, R. B., Cano, J. M., & Merilä, J. (2007) · Journal of Evolutionary Biology · doi:10.1111/j.1420-9101.2007.01445.x · Cited by 528 · see citing works
Markov chain Monte Carlo method and its application
Brooks, S. (1998) · Journal of the Royal Statistical Society: Series D (The Statistician) · doi:10.1111/1467-9884.00117 · Cited by 843 · see citing works
Self-citationLambert, P. C., Sutton, A. J., Burton, P. R., Abrams, K. R., & Jones, D. R. (2005) · Statistics in Medicine · doi:10.1002/sim.2112 · Cited by 511 · see citing works
Population Pharmacokinetics of Therapeutic Monoclonal Antibodies
Dirks, N. L., & Meibohm, B. (2010) · Clinical Pharmacokinetics · doi:10.2165/11535960-000000000-00000 · Cited by 500 · see citing works
Price, M. J., Ades, A., Soldan, K., Welton, N. J., Macleod, J., Simms, I., DeAngelis, D., Turner, K. M., & Horner, P. J. (2016) · Health Technology Assessment · doi:10.3310/hta20220 · Cited by 494 · see citing works
Wilson, A. M., & Jetz, W. (2016) · PLoS Biology · doi:10.1371/journal.pbio.1002415 · Cited by 488 · see citing works
Xie, X., Liu, Y., Perkovic, V., Li, X., Ninomiya, T., Hou, W., Zhao, N., Liu, L., Lv, J., Zhang, H., et al. (2015) · American Journal of Kidney Diseases · doi:10.1053/j.ajkd.2015.10.011 · Cited by 484 · see citing works
Cosmological parameters from the BOSS galaxy power spectrum
Ivanov, M. M., Simonović, M., & Zaldarriaga, M. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/05/042 · Cited by 477 · see citing works
Frailty Models in Survival Analysis
Wienke, A. (2010) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420073911 · Cited by 474 · see citing works
Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem
Malinverno, A. (2002) · Geophysical Journal International · doi:10.1046/j.1365-246x.2002.01847.x · Cited by 470 · see citing works
Convergence assessment techniques for Markov chain Monte Carlo
Brooks, S. P., & Roberts, G. O. (1998) · Statistics and Computing · doi:10.1023/a:1008820505350 · Cited by 464 · see citing works
Self-citationMatzke, D., & Wagenmakers, E. (2009) · Psychonomic Bulletin & Review · doi:10.3758/pbr.16.5.798 · Cited by 462 · see citing works
Genetic Variation in Preferences for Giving and Risk Taking *
Cesarini, D. A., Dawes, C. T., Johannesson, M., Lichtenstein, P., & Wallace, B. (2009) · The Quarterly Journal of Economics · doi:10.1162/qjec.2009.124.2.809 · Cited by 460 · see citing works
Bayesian Analysis Reporting Guidelines
Kruschke, J. K. (2021) · Nature Human Behaviour · doi:10.1038/s41562-021-01177-7 · Cited by 462 · see citing works
Epidemiology of fragile X syndrome: A systematic review and meta‐analysis
Hunter, J. E., Rivero‐Arias, O., Angelov, A., Kim, E., Fotheringham, I., & Leal, J. (2014) · American Journal of Medical Genetics Part A · doi:10.1002/ajmg.a.36511 · Cited by 446 · see citing works
Nonlinear Unmixing of Hyperspectral Images Using a Generalized Bilinear Model
Halimi, A., Altmann, Y., Dobigeon, N., & Tourneret, J. (2011) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2010.2098414 · Cited by 443 · see citing works
A Bayesian approach to inferring population structure from dominant markers
Holsinger, K. E., Lewis, P. O., & Dey, D. K. (2002) · Molecular Ecology · doi:10.1046/j.1365-294x.2002.01512.x · Cited by 443 · see citing works
A two decade dementia incidence comparison from the Cognitive Function and Ageing Studies I and II
Matthews, F. E., Stephan, B. C. M., Robinson, L., Jagger, C., Barnes, L. E., Arthur, A., Brayne, C., Cognitive Function and Ageing Studies (CFAS) Collaboration, Comas-Herrera, A., Wittenberg, R., et al. (2016) · Nature Communications · doi:10.1038/ncomms11398 · Cited by 426 · see citing works
Martin, J. L., Wilcox, L. C., Burstedde, C., & Ghattas, O. N. (2012) · SIAM Journal on Scientific Computing · doi:10.1137/110845598 · Cited by 424 · see citing works
Reconstruction of the full transmission dynamics of COVID-19 in Wuhan
Hao, X., Cheng, S., Wu, D., Wu, T., Lin, X., & Wang, C. (2020) · Nature · doi:10.1038/s41586-020-2554-8 · Cited by 419 · see citing works
Storz, J. F., & Beaumont, M. (2002) · Evolution · doi:10.1111/j.0014-3820.2002.tb00857.x · Cited by 414 · see citing works
Unveiling ν secrets with cosmological data: Neutrino masses and mass hierarchy
Vagnozzi, S., Giusarma, E., Mena, O., Katherine Freese, B., Gerbino, M., Ho, S., & Lattanzi, M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.123503 · Cited by 411 · see citing works
Shallue, C. J., & Vanderburg, A. M. (2018) · The Astronomical Journal · doi:10.3847/1538-3881/aa9e09 · Cited by 409 · see citing works
Turner, R. M., Jackson, D., Wei, Y., Thompson, S. G., & Higgins, J. P. T. (2015) · Statistics in Medicine · doi:10.1002/sim.6381 · Cited by 410 · see citing works
Zheng, S. L., Roddick, A., Agha-Jaffar, R., Shun-Shin, M. J., Francis, D. P., Oliver, N. S., & Meeran, K. M. (2018) · JAMA · doi:10.1001/jama.2018.3024 · Cited by 402 · see citing works
Joint Species Distribution Modelling
Ovaskainen, O., & Abrego, N. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108591720 · Cited by 404 · see citing works
Rhodes, K. M., Turner, R., & Higgins, J. P. T. (2014) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2014.08.012 · Cited by 398 · see citing works
Brain size predicts problem-solving ability in mammalian carnivores
Benson‐Amram, S., Dantzer, B., Stricker, G., Swanson, E. M., & Holekamp, K. E. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1505913113 · Cited by 394 · see citing works
Uthman, O. A., van der Windt, D., Jordan, J. L., Dziedzic, K., Healey, E. L., Peat, G., & Foster, N. E. (2013) · BMJ · doi:10.1136/bmj.f5555 · Cited by 379 · see citing works
Levosimendan for the Prevention of Acute Organ Dysfunction in Sepsis
Gordon, A. C., Perkins, G. D., Singer, M., McAuley, D. F., Orme, R. M. L., Santhakumaran, S., Mason, A. J., Cross, M., Al-Beidh, F., Best-Lane, J., et al. (2016) · New England Journal of Medicine · doi:10.1056/nejmoa1609409 · Cited by 372 · see citing works
Coudeville, L., Bailleux, F., Riche, B., Megas, F., Andre, P., & Écochard, R. (2010) · BMC Medical Research Methodology · doi:10.1186/1471-2288-10-18 · Cited by 376 · see citing works
Huang, H., Chin, H. C., & Haque, M. M. (2007) · Accident Analysis & Prevention · doi:10.1016/j.aap.2007.04.002 · Cited by 373 · see citing works
Christoffel, K. P., Coenen, G., & Warne, A. (2008) · SSRN Electronic Journal · doi:10.2139/ssrn.1271865 · Cited by 373 · see citing works
Zhou, X., Teng, T., Zhang, Y., Del Giovane, C., Furukawa, T. A., Weisz, J. R., Li, X., Cuijpers, P., Coghill, D., Xiang, Y., et al. (2020) · The Lancet Psychiatry · doi:10.1016/s2215-0366(20)30137-1 · Cited by 367 · see citing works
Network Meta-Analysis Using R: A Review of Currently Available Automated Packages
Neupane, B., Richer, D., Bonner, A., Kibret, T. C., & Beyene, J. (2014) · PLoS ONE · doi:10.1371/journal.pone.0115065 · Cited by 366 · see citing works
Welton, N. J., Caldwell, D. M., Adamopoulos, E., & Vedhara, K. (2009) · American Journal of Epidemiology · doi:10.1093/aje/kwp014 · Cited by 360 · see citing works
Windecker, S., Stortecky, S., Stefanini, G. G., daCosta, B. R., Rutjes, A. W., Nisio, M. D., Siletta, M., Maione, A., Alfonso, F., Clemmensen, P. M., et al. (2014) · BMJ · doi:10.1136/bmj.g3859 · Cited by 357 · see citing works
Link, W. A., & Eaton, M. J. (2012) · Methods in Ecology and Evolution · doi:10.1111/j.2041-210x.2011.00131.x · Cited by 351 · see citing works
Gregori, D., Giacovelli, G., Minto, C., Barbetta, B., Gualtieri, F., Azzolina, D., Vaghi, P., & Rovati, L. C. (2018) · JAMA · doi:10.1001/jama.2018.19319 · Cited by 338 · see citing works
A Bayesian Approach to Quantify the Contribution of Animal‐Food Sources to Human Salmonellosis
Hald, T., Vose, D., Wegener, H. C., & Koupeev, T. (2004) · Risk Analysis · doi:10.1111/j.0272-4332.2004.00427.x · Cited by 335 · see citing works
Monetary policy and uncertainty in an empirical small open‐economy model
Justiniano, A., & Preston, B. (2010) · Journal of Applied Econometrics · doi:10.1002/jae.1153 · Cited by 334 · see citing works
How Many Bootstrap Replicates Are Necessary?
Pattengale, N. D., Alipour, M., Bininda‐Emonds, O. R. P., Moret, B. M. E., & Stamatakis, A. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-02008-7_13 · Cited by 333 · see citing works
Hadfield, J. D., Richardson, D. S., & Burke, T. A. (2006) · Molecular Ecology · doi:10.1111/j.1365-294x.2006.03050.x · Cited by 332 · see citing works
Zhou, X., Hetrick, S. E., Cuijpers, P., Qin, B., Barth, J., Whittington, C. J., Cohen, D., Del Giovane, C., Liu, Y., Michael, K. D., et al. (2015) · World Psychiatry · doi:10.1002/wps.20217 · Cited by 322 · see citing works
QUEST III: An estimated open-economy DSGE model of the euro area with fiscal and monetary policy
Ratto, M., Roeger, W., & Veld, J. I. ’. (2008) · Economic Modelling · doi:10.1016/j.econmod.2008.06.014 · Cited by 322 · see citing works
Polytomies and Bayesian Phylogenetic Inference
Lewis, P. O., Holder, M. T., & Holsinger, K. E. (2005) · Systematic Biology · doi:10.1080/10635150590924208 · Cited by 318 · see citing works
Bayesian inference of ancestral dates on bacterial phylogenetic trees
Didelot, X., Croucher, N. J., Bentley, S. D., Harris, S. R., & Wilson, D. J. (2018) · Nucleic Acids Research · doi:10.1093/nar/gky783 · Cited by 317 · see citing works
Isayama, T., Iwami, H., McDonald, S. D., & Beyene, J. (2016) · JAMA · doi:10.1001/jama.2016.10708 · Cited by 310 · see citing works
A Global Measure of Judicial Independence, 1948–2012
Linzer, D. A., & Staton, J. K. (2015) · Journal of Law and Courts · doi:10.1086/682150 · Cited by 305 · see citing works
A design‐by‐treatment interaction model for network meta‐analysis with random inconsistency effects
Jackson, D., Barrett, J., Rice, S. J. C., White, I. R., & Higgins, J. P. T. (2014) · Statistics in Medicine · doi:10.1002/sim.6188 · Cited by 306 · see citing works
Comparing Bootstrap and Posterior Probability Values in the Four-Taxon Case
Cummings, M. P., Handley, S. A., Myers, D. S., Reed, D. L., Rokas, A., & Winka, K. (2003) · Systematic Biology · doi:10.1080/10635150390218213 · Cited by 306 · see citing works
Vlaar, P. J. J., Mahmoud, K. D., Holmes, D. R., van Valkenhoef, G., Hillege, H. L., van der Horst, I. C. C., Zijlstra, F., & de Smet, B. J. G. L. (2011) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2011.03.046 · Cited by 305 · see citing works
Inference in Molecular Population Genetics
Stephens, M., & Donnelly, P. (2000) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00254 · Cited by 301 · see citing works
Analysis of Multinomial Models With Unknown Index Using Data Augmentation
Royle, J. A., Dorazio, R. M., & Link, W. A. (2007) · Journal of Computational and Graphical Statistics · doi:10.1198/106186007x181425 · Cited by 301 · see citing works
Convergence Diagnostics for Markov Chain Monte Carlo
Roy, V. (2019) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-031219-041300 · Cited by 301 · see citing works
Heritability of cooperative behavior in the trust game
Cesarini, D., Dawes, C. T., Fowler, J. H., Johannesson, M., Lichtenstein, P., & Wallace, B. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0710069105 · Cited by 371 · see citing works
Effat, M. B., & Francesco Ciucci, A. (2017) · Electrochimica Acta · doi:10.1016/j.electacta.2017.07.050 · Cited by 298 · see citing works
Systems-level analysis of mechanisms regulating yeast metabolic flux
Hackett, S. R., Zanotelli, V. R., Xu, W., Goya, J., Park, J. O., Perlman, D. H., Gibney, P. A., Botstein, D., Storey, J. D., & Rabinowitz, J. D. (2016) · Science · doi:10.1126/science.aaf2786 · Cited by 297 · see citing works
Multilevel data and Bayesian analysis in traffic safety
Huang, H., & Abdel-Aty, M. A. (2010) · Accident Analysis & Prevention · doi:10.1016/j.aap.2010.03.013 · Cited by 295 · see citing works
A Prospective Study of Chronic Pain after Thoracic Surgery
Bayman, E. O., Parekh, K. R., Keech, J. C., Selte, A., & Brennan, T. J. (2017) · Anesthesiology · doi:10.1097/aln.0000000000001576 · Cited by 285 · see citing works
Nguyen, M., & Jones, T. (2022) · Humanities and Social Sciences Communications · doi:10.1057/s41599-022-01441-9 · Cited by 282 · see citing works
Dynare: Reference Manual. Version 4
Adjemian, S., Bastani, H., Juillard, M., Mihoubi, F., Perendia, G., Marco, R., & Sébastien, V. (2011) · Joint Research Centre (European Commission) · Cited by 282 · see citing works
Nguyen, M., La, V., Le, T.-T., & Vuong, Q. (2022) · MethodsX · doi:10.1016/j.mex.2022.101808 · Cited by 269 · see citing works
County-Level Crash Risk Analysis in Florida: Bayesian Spatial Modeling
Huang, H., Abdel-Aty, M. A., & Darwiche, A. L. (2010) · Transportation Research Record Journal of the Transportation Research Board · doi:10.3141/2148-04 · Cited by 275 · see citing works
Edwards, J. J., Deenmamode, A. H. P., Griffiths, M., Arnold, O., Cooper, N. J., Wiles, J. D., & O'Driscoll, J. M. (2023) · British Journal of Sports Medicine · doi:10.1136/bjsports-2022-106503 · Cited by 284 · see citing works
Plant hydraulics accentuates the effect of atmospheric moisture stress on transpiration
Liu, Y., Kumar, M., Katul, G. G., Feng, X. D., & Konings, A. G. (2020) · Nature Climate Change · doi:10.1038/s41558-020-0781-5 · Cited by 273 · see citing works
Schmidt, B. R., Kéry, M., Ursenbacher, S., Hyman, O. J., & Collins, J. P. (2013) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12052 · Cited by 270 · see citing works
- 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
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
