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Stan : A Probabilistic Programming Language
Open accessAbstract
Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.
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“When dealing with more complex models that go beyond the staple analyses such as t tests, there exist a number of software packages that allow custom coding, such as JAGS (Plummer, 2003) or Stan (Carpenter et al., 2017).”
From The JASP guidelines for conducting and reporting a Bayesian analysis (2021) · cites this paper as Carpenter et al., 2017
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On the Use of Mixed Markov Models for Intensive Longitudinal Data
de Haan-Rietdijk, S., Kuppens, P., Bergeman, C. S., Sheeber, L., Allen, N. B., & Hamaker, E. L. (2017) · Multivariate Behavioral Research · doi:10.1080/00273171.2017.1370364 · Cited by 44
The effect of thinning on mechanical properties of Douglas fir, Norway spruce, and Sitka spruce
Krajnc, L., Farrelly, N., & Harte, A. M. (2019) · Annals of Forest Science · doi:10.1007/s13595-018-0787-6 · Cited by 44
“N Z J For Sci 45(1), DOI 10.1186/s40490-015-0053-8 577 Kruschke J (2014) Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, 2nd 578 edn.”
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“A No-U-Turn sampler (NUTS) Marcov Chain Monte Carlo (MCMC) algorithm, implemented using the Pystan package (Carpenter et al. 2017) in the Python programming language, was used to estimate the posterior probability distribution.”
MethodBürgy, L., Eicke, S., Kopp, C., et al. (2021) · Nature Communications · doi:10.1038/s41467-021-27151-5 · Cited by 44
On the convergence of Hamiltonian Monte CarloPreprint
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Whittaker, C., Hamlet, A., Sherrard-Smith, E., Winskill, P., Cuomo-Dannenburg, G., Walker, P. G. T., Sinka, M., Pironon, S., Kumar, A., Ghani, A., et al. (2023) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2216142120 · Cited by 43
Test-retest reliability and sample size estimates after MRI scanner relocation
Melzer, T. R., Keenan, R. J., Leeper, G. J., Kingston-Smith, S., Felton, S. A., Green, S. K., Henderson, K. J., Palmer, N. J., Shoorangiz, R., Almuqbel, M. M., et al. (2020) · NeuroImage · doi:10.1016/j.neuroimage.2020.116608 · Cited by 43
“9.0) package (Buerkner, 2017; Carpenter et al., 2017) in R (v3.”
BackgroundInfluentialMatamoros, C. I., Klopp, R. N., Moraes, L. E., & Harvatine, K. J. (2020) · Journal of Dairy Science · doi:10.3168/jds.2019-18129 · Cited by 43
“All models were fitted in Stan using the Hamiltonian Monte Carlo No-U-Turn Sampler (Carpenter et al., 2017) through the rstan package of R version 3.”
MethodInfluentialRemiro‐Azócar, A., Heath, A., & Baio, G. (2022) · Research Synthesis Methods · doi:10.1002/jrsm.1565 · Cited by 46
Wildlife impacts and changing climate pose compounding threats to human food security
Salerno, J., Stevens, F. R., Gaughan, A. E., Hilton, T., Bailey, K. M., Bowles, T. M., Cassidy, L., Mupeta‐Muyamwa, P., Biggs, D., Pricope, N. G., et al. (2021) · Current Biology · doi:10.1016/j.cub.2021.08.074 · Cited by 48
A practical guide to understanding and validating complex models using data simulations
DiRenzo, G. V., Hanks, E. M., & Miller, D. A. W. (2022) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.14030 · Cited by 50
“Second, more biologists are learning to use flexible programming languages that facilitate writing tailored complex hierarchical models (e.g. BUGS Sturtz et al., 2005 , JAGS Plummer, 2003, stan Carpenter et al., 2017 , package lme 4 Bates et al., 2015, machine learning methods Joseph, 2020 ).”
BackgroundVilla, S., Kosch, T., Grelka, F., Schmidt, A., & Welsch, R. (2023) · Computers in Human Behavior · doi:10.1016/j.chb.2023.107787 · Cited by 49
“We used an R-Net 64-channel EEG with a wireless amplifier. the STAN-sampler (Carpenter et al., 2017).”
MethodBayesian hierarchical modeling: an introduction and reassessment
Veenman, M., Stefan, A. M., & Haaf, J. M. (2023) · Behavior Research Methods · doi:10.3758/s13428-023-02204-3 · Cited by 64
“For rstan , we recommend the Stan manual (Stan Development Team, 2018a, 2018b).”
BackgroundInfluentialEvidential Strength of Intonational Cues and Rational Adaptation to (Un‐)Reliable Intonation
Roettger, T. B., & Franke, M. (2019) · Cognitive Science · doi:10.1111/cogs.12745 · Cited by 43
Black swans in space: modeling spatiotemporal processes with extremes
Anderson, S. C., & Ward, E. J. (2018) · Ecology · doi:10.1002/ecy.2403 · Cited by 43
Measuring and interpreting relationships between nutrient supply, demand, and limitation
Covino, T. P., Bernhardt, E. S., & Heffernan, J. B. (2018) · Freshwater Science · doi:10.1086/699202 · Cited by 43
“The model was fit through R (version 3.2.3; R Project for Statistical Computing, Vienna, Austria) with Markov Chain Monte Carlo (MCMC) sampling (Carpenter et al. 2017).”
MethodInfluentialSimulating Active Inference Processes by Message Passing
van de Laar, T., & de Vries, B. (2019) · Frontiers in Robotics and AI · doi:10.3389/frobt.2019.00020 · Cited by 43
“Recent state-of-the-art PP toolboxes such as Stan (Carpenter et al., 2017), Edward (Tran et al.”
BackgroundMethodSpatial variation in exploited metapopulations obscures risk of collapse
Okamoto, D. K., Hessing-Lewis, M. L., Samhouri, J. F., Shelton, A. O., Stier, A. C., Levin, P. S., & Salomon, A. K. (2019) · Ecological Applications · doi:10.1002/eap.2051 · Cited by 45
Blumstein, M., Richardson, A. D., Weston, D. J., Zhang, J., Muchero, W., & Hopkins, R. (2020) · Current Biology · doi:10.1016/j.cub.2020.02.001 · Cited by 43
Fiel, J. E. (2020) · Sociology of Education · doi:10.1177/0038040720927886 · Cited by 44
“1), which uses Hamiltonian Monte Carlo sampling, an efficient simulation method for complex Bayesian models (Carpenter et al. 2017; Gelman et al. 2013).”
MethodInfluentialPinto‐Ledezma, J. N., Villalobos, F., Reich, P. B., Catford, J. A., Larkin, D. J., & Cavender-Bares, J. M. (2020) · Ecological Monographs · doi:10.1002/ecm.1420 · Cited by 43
Effect of pelagic longline bait type on species selectivity: a global synthesis of evidence
Gilman, E. L., Chaloupka, M. Y., Bach, P., Fennell, H., Hall, M. A., Musyl, M. K., Piovano, S., Poisson, F., & Song, L. (2020) · Reviews in Fish Biology and Fisheries · doi:10.1007/s11160-020-09612-0 · Cited by 51
Diersch, N., Valdés-Herrera, J. P., Tempelmann, C., & Wolbers, T. (2021) · Journal of Neuroscience · doi:10.1523/jneurosci.0528-20.2021 · Cited by 46
Predicting species distributions and community composition using satellite remote sensing predictors
Pinto‐Ledezma, J. N., & Cavender-Bares, J. M. (2021) · Scientific Reports · doi:10.1038/s41598-021-96047-7 · Cited by 48
van de Sande, J., Vaughan, S. P., Cortese, L., Scott, N., Bland‐Hawthorn, J., Croom, S. M., Lagos, C. D. P., Brough, S., Bryant, J. J., Devriendt, J., et al. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab1490 · Cited by 43
Bored, distracted, and forgetful: The impact of mind wandering and boredom on memory encoding
Blondé, P., Sperduti, M., Makowski, D., & Piolino, P. (2021) · Quarterly Journal of Experimental Psychology · doi:10.1177/17470218211026301 · Cited by 55
“In line with recent statistical guidelines (Etz & Vandekerckhove, 2016; Wagenmakers et al., 2018), we used the Bayesian framework to analyse our data, using the packages rstanarm (Carpenter et al., 2017; Gabry & Goodrich, 2016) and psycho (Makowski, 2018).”
MethodReconstruction of plant–pollinator networks from observational data
Young, J.-G., Valdovinos, F. S., & Newman, M. E. J. (2021) · Nature Communications · doi:10.1038/s41467-021-24149-x · Cited by 43
Hashemi, M., Vattikonda, A. N., Ší́p, V., Diaz-Pier, S., Peyser, A., Wang, H., Guye, M., Bartoloméi, F., Woodman, M., & Jirsa, V. (2021) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1009129 · Cited by 39
“The figure plots the averages over 4 HMC chains randomly initialized in search space.”
MethodInfluentialSPPL: probabilistic programming with fast exact symbolic inference
Saad, F. A., Rinard, M., & Mansinghka, V. K. (2021) · ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI) · doi:10.1145/3453483.3454078 · Cited by 42
“A terminal node Leaf( 𝑥 𝑑 𝜎 ) is comprised of a Var 𝑥 , Distribution 𝑑 , and Environment 𝜎 that maps other variables to a Transform of 𝑥 , e.g., Z ↦→ Poly(Root(Id(X) 2 ) [ 11 , 5 ] ) .”
BackgroundDoes the Ideology of the Newsroom Affect the Provision of Media Slant?
Hassell, H. J. G., Miles, M. R., & Reuning, K. (2021) · Political Communication · doi:10.1080/10584609.2021.1986613 · Cited by 42
Smit, E. A., Milne, A. J., Sarvasy, H. S., & Dean, R. T. (2022) · PLoS ONE · doi:10.1371/journal.pone.0269597 · Cited by 46
“Lyn Ögate, Stanly Girip, and James Jio were the highly efficient organizers of the Towet ‘research fair’ of which this experiment formed a part.”
MethodUlitzsch, E., Shin, H. J., & Lüdtke, O. (2023) · Behavior Research Methods · doi:10.3758/s13428-022-02053-6 · Cited by 42
“Bayesian estimation of the Beta regression was conducted using Stan version 2.19 (Carpenter et al., 2017) employing the rstan package version 2.19.3 (Guo, Gabry, & Goodrich, 2018).”
MethodInfluentialNoradrenaline tracks emotional modulation of attention in human amygdala
Bang, D., Luo, Y., Barbosa, L. S., Batten, S. R., Hadj-Amar, B., Twomey, T., Melville, N., White, J. P., Torres, A. S., Celaya, X., et al. (2023) · Current Biology · doi:10.1016/j.cub.2023.09.074 · Cited by 43
Modrák, M., Moon, A. H., Kim, S., Bürkner, P., Huurre, N., Faltejsková, K., Gelman, A., & Vehtari, A. (2025) · Bayesian Analysis · doi:10.1214/23-ba1404 · Cited by 42
“SBC-like checks The identity of prior and posterior distributions conditional on a specific dataset as a tool to check computation was proposed by Cook et al. (2006) and further refined by Talts et al. (2020) who introduced SBC as it is currently used.”
MethodInfluentialSelf-citationLikelihood-based parameter estimation and comparison of dynamical cognitive models.
Schütt, H. H., Rothkegel, L. O. M., Trukenbrod, H. A., Reich, S., Wichmann, F. A., & Engbert, R. (2017) · Psychological Review · doi:10.1037/rev0000068 · Cited by 44
“ee Neal, 2011, for an introduction). By now there are many variants of HMC available, including adaptive methods like the No-U-turn Sampler (NUTS, Homan & Gelman, 2014), which works behind STAN (Carpenter et al., 2016), one of the most recent general purpose samplers. These samplers contain automatic dierentiation…”
MethodShelton, A. O., Satterthwaite, W. H., Ward, E. J., Feist, B. E., & Burke, B. J. (2018) · Canadian Journal of Fisheries and Aquatic Sciences · doi:10.1139/cjfas-2017-0204 · Cited by 44
Using Hamiltonian Monte Carlo to estimate the log-linear cognitive diagnosis model via Stan
Jiang, Z., & Carter, R. A. (2018) · Behavior Research Methods · doi:10.3758/s13428-018-1069-9 · Cited by 43
Lindström, H. J. G., & Friedman, R. (2020) · BMC Cancer · doi:10.1186/s12885-020-06782-9 · Cited by 41
Disentangling vulnerability, state and trait features of neurocognitive impairments in depression
Ang, Y., Frontero, N., Belleau, E. L., & Pizzagalli, D. A. (2020) · Brain · doi:10.1093/brain/awaa314 · Cited by 41
“Estimation is conducted in Stan (Carpenter et al., 2017) using the Hamiltonian Monte Carlo algorithm extension, No-U-Turn Sampler (Hoffman and Gelman, 2014).”
MethodThermal stability of cannabinoids in dried cannabis: a kinetic study
Meija, J., McRae, G., Miles, C. O., et al. (2021) · Analytical and Bioanalytical Chemistry · doi:10.1007/s00216-020-03098-2 · Cited by 42
“We chose STAN largely due to its ability to handle differential equations [19].”
MethodHopkins, A. K., Dolan, R. J., Button, K. S., & Moutoussis, M. (2021) · Computational Psychiatry · doi:10.5334/cpsy.57 · Cited by 42
“Based on the literature (Carpenter et al., 2017) and the theory of self-schema, we examined the specific hypotheses that BFNE would relate to the trait-evidence in the self schema (αself and/or βself) or the corresponding learning rates λself,+ve and λself,-ve (See supplement for the theoretical derivation of this app…”
InfluentialBacterial genomic epidemiology with mixed samples
Mäklin, T., Kallonen, T., Alanko, J., Samuelsen, Ø., Hegstad, K., Mäkinen, V., Corander, J., Heinz, E., & Honkela, A. (2021) · Microbial Genomics · doi:10.1099/mgen.0.000691 · Cited by 40
Kocher, A., Cornuault, J., Gantier, J.-C., Manzi, S., Chavy, A., Girod, R., Dusfour, I., Forget, P., Ginouvès, M., Prévot, G., et al. (2022) · Molecular Ecology · doi:10.1111/mec.16341 · Cited by 42
Brown, V. M., Hallquist, M. N., Frank, M. J., & Dombrovski, A. Y. (2022) · Cognition · doi:10.1016/j.cognition.2022.105233 · Cited by 51
Shape of U: The Nonmonotonic Relationship Between Object–Location Memory and Expectedness
Quent, J. A., Greve, A., & Henson, R. N. (2022) · Psychological Science · doi:10.1177/09567976221109134 · Cited by 42
“Statistical analysis was performed in R (R Core Team, 2018) using Bayesian multilevel models with brms (Bürkner, 2018, version 2.16.3) based on Stan (Carpenter et al., 2017).”
MethodInfluentialBürkner, P.-C., Bittner, N., Holling, H., & Buhlmann, U. (2017) · PLoS ONE · doi:10.1371/journal.pone.0173660 · Cited by 41
“The packagemetafor [67] was used for the effect size computation, while the package brms [68]–allowing to fit Bayesian multilevel models (including meta-analytic models) using Stan [69]–was used for the actual analysis.”
Methodvon der Malsburg, T., Poppels, T., & Lévy, R. (2020) · Psychological Science · doi:10.1177/0956797619890619 · Cited by 41
“Analyses were conducted using Bayesian hierarchical generalized linear models with maximal random-effects structure (Barr, Levy, Scheepers, & Tily, 2013) implemented in the Stan system for full Bayesian inference (Carpenter et al., 2017).”
MethodPartial migration of White-winged snowfinches is correlated with winter weather conditions
Resano‐Mayor, J., Bettega, C., Delgado, M. D. M., et al. (2020) · Global Ecology and Conservation · doi:10.1016/j.gecco.2020.e01346 · Cited by 41
A Principled Approach to Feature Selection in Models of Sentence Processing
Smith, G., & Vasishth, S. (2020) · Cognitive Science · doi:10.1111/cogs.12918 · Cited by 41
Estimating predator functional responses using the times between prey captures
Coblentz, K. E., & DeLong, J. P. (2021) · Ecology · doi:10.1002/ecy.3307 · Cited by 41
Strain Identification and Quantitative Analysis in Microbial Communities
Ghazi, A. R., Münch, P. C., Chen, D., Jensen, J., & Huttenhower, C. (2022) · Journal of Molecular Biology · doi:10.1016/j.jmb.2022.167582 · Cited by 44
Reconstruction of GRACE Mass Change Time Series Using a Bayesian Framework
Rateb, A., Sun, A. Y., Scanlon, B. R., Save, H. V., & Hasan, E. (2022) · Earth and Space Science · doi:10.1029/2021ea002162 · Cited by 40
“The computation was carried out using Stan probablistic programming (Carpenter et al., 2017), using R interface (Team, 2013).”
MethodMadsen, L. J., & Royle, J. A. (2023) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.1625 · Cited by 41
“The R package ubms (Kellner et al., 2022) is another option for Bayesian analysis which uses an unmarked-like formula interface but STAN (Carpenter et al., 2017) as the back-end computing engine.”
MethodSEAM: An Integrated Activation-Coupled Model of Sentence Processing and Eye Movements in Reading
Rabe, M., Paape, D., Mertzen, D., Vasishth, S., & Engbert, R. (2023) · Journal of Memory and Language · doi:10.1016/j.jml.2023.104496 · Cited by 26
“The models were implemented with brms (Bürkner, 2017, 2018, 2021), an interface to Stan (Carpenter et al., 2017).”
MethodPedroza, C., & Truong, V. T. T. (2017) · Trials · doi:10.1186/s13063-017-2248-1 · Cited by 44
“Stan Development Team.”
MethodInfluentialSilk, M. J., Drewe, J. A., Delahay, R. J., Weber, N. L., Steward, L. C., Wilson‐Aggarwal, J. K., Boots, M., Hodgson, D. J., Croft, D. P., & McDonald, R. A. (2018) · Behaviour · doi:10.1163/1568539x-00003493 · Cited by 41
Deliberation and Procedural Automation on a Two-Step Task for Rats
Hasz, B. M., & Redish, A. D. (2018) · Frontiers in Integrative Neuroscience · doi:10.3389/fnint.2018.00030 · Cited by 46
“To more rigorously evaluate model-based or model-free influences on rat choices, we fit model-based and model-free algorithms to rat choices on the two-step task using Stan, in order to perform Bayesian inference and compare models (Kruschke, 2014; Carpenter et al., 2017).”
MethodAdeloye, D., Harhay, M. O., Ayepola, O. O., Santos, J. P. D., David, R. A., Ogunlana, O. O., Gadanya, M. A., Osamor, V. C., Amuta, A. O., Iweala, E., et al. (2018) · International Journal of Urology · doi:10.1111/iju.13824 · Cited by 41
“All statistical analyses were conducted using the package rstan (probabilistic programming language) in the R programming language (see Supporting methods).(19)”
MethodRadersma, R., Hegg, A., Noble, D. W. A., & Uller, T. (2018) · Ecology and Evolution · doi:10.1002/ece3.4700 · Cited by 41
Bayesian inference of protein conformational ensembles from limited structural data
Potrzebowski, W., Trewhella, J., & André, I. (2018) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006641 · Cited by 41
The dynamics of intonation: Categorical and continuous variation in an attractor-based model
Roessig, S., Mücke, D., & Grice, M. (2019) · PLoS ONE · doi:10.1371/journal.pone.0216859 · Cited by 41
Dissociating refreshing and elaboration and their impacts on memory
Bartsch, L. M., Loaiza, V. M., Jäncke, L., Oberauer, K., & Lewis‐Peacock, J. A. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2019.06.028 · Cited by 44
“We used an MCMC algorithm (implemented in Stan; Carpenter et al., 2017) that estimated the posteriors by sampling parameter values proportional to the product of prior and likelihood.”
MethodBertola, M., Viglione, A., & Blöschl, G. (2019) · Journal of Hydrology · doi:10.1016/j.jhydrol.2019.123919 · Cited by 39
“RStan makes use of Hamiltonian Monte Carlo sampling, which speeds up convergence and parameter exploration by using the gradient of the log posterior (Stan Development Team, 2018).”
MethodWright, W. J., Irvine, K. M., Almberg, E. S., et al. (2019) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.13315 · Cited by 41
“Ecology, 86(9), 2505–2512. https ://doi.org/10.1890/04-1802 Stan Development Team.”
MethodInfluentialThe Hastings algorithm at fifty
Dunson, D. B., & Johndrow, J. E. (2019) · Biometrika · doi:10.1093/biomet/asz066 · Cited by 41
Altitudinal upwards shifts in fungal fruiting in the Alps
Diez, J. M., Kauserud, H., Andrew, C. J., Heegaard, E., Krisai‐Greilhüber, I., Senn-Irlet, B., Høiland, K., Egli, S., & Büntgen, U. (2020) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2019.2348 · Cited by 43
“All models were fitted in a Bayesian framework using the brms package [28] in R [29], which uses Stan software [30] for parameter estimation.”
MethodRose, B. M., Rubin, D., Cikota, A., Deustua, S. E., Dixon, S., Fruchter, A. S., Jones, D. O., Riess, A. G., & Scolnic, D. M. (2020) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab94ad · Cited by 41
“…Numpy (van der Walt et al. 2011), Pandas (McKinney 2010), pystan (https://doi.org/10.5281/zenodo.598257), python, SciPy (Jones et al. 2001), stan (Carpenter et al. 2017), UNITY (Rubin et al. 2015), ZPEG (Le Borgne & RoccaVolmerange 2002) REFERENCES Betoule, M., Kessler, R., Guy, J., et al. 2014,…”
InfluentialRapid, precise, and reliable measurement of delay discounting using a Bayesian learning algorithm
Ahn, W., Gu, H., Shen, Y. I., Haines, N., Hahn, H. A., Teater, J. E., Myung, J. I., & Pitt, M. A. (2020) · Scientific Reports · doi:10.1038/s41598-020-68587-x · Cited by 41
“com/CCSLab/hBayesDM) offers hierarchical and non-hierarchical Bayesian analysis of various computational models and tasks using the Stan software (Carpenter et al., 2016).”
MethodBAT.jl: A Julia-Based Tool for Bayesian Inference
Schulz, O., Beaujean, F., Caldwell, A. C., Grunwald, C., Hafych, V., Kroeninger, K. A., Cagnina, S. L., Röhrig, L., & Shtembari, L. (2021) · SN Computer Science · doi:10.1007/s42979-021-00626-4 · Cited by 41
“A variety of automated tools are available, usually tailored to the needs of a particular field of research or a class of statistical models, such as STAN [7], PYMC [8], R [9] or OpenBUGS [10].”
MethodImputation of Ordinal Outcomes: A Comparison of Approaches in Traumatic Brain Injury
Kunzmann, K., Wernisch, L., Richardson, S. T., Steyerberg, E. W., Lingsma, H. F., Ercole, A., Maas, A. I. R., Menon, D. K., & Wilson, L. (2020) · Journal of Neurotrauma · doi:10.1089/neu.2019.6858 · Cited by 40
Armstrong, M. K., Fraser, B. J., Hartiala, O., Buscot, M., Juonala, M., Wu, F., Koskinen, J. M., Hutri‐Kähönen, N., Kähönen, M. A. P., Laitinen, T. P., et al. (2021) · JAMA Cardiology · doi:10.1001/jamacardio.2020.7238 · Cited by 41
Intrusive memories as conditioned responses to trauma cues: An empirically supported concept?
Franke, L. K., Rattel, J. A., Miedl, S. F., Danböck, S. K., Bürkner, P., & Wilhelm, F. H. (2021) · Behaviour Research and Therapy · doi:10.1016/j.brat.2021.103848 · Cited by 46
A Cognitive-Emotional Model to Explain Message Framing Effects: Reducing Meat Consumption
Carfora, V., Pastore, M., & Catellani, P. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.583209 · Cited by 48
“Data Analysis We adopted a fully Bayesian approach (Kruschke and Liddell, 2017) and all analyses were performed with the R software and programming language (R Development Core Team, 2016), with the rstan (Carpenter et al., 2017; Stan Development Team, 2018) and blavaan (Merkle and Rosseel, 2015) packages.”
Methodvan Oostrum, I., Ouwens, M., Remiro‐Azócar, A., Baio, G., Postma, M. J., Buskens, E., & Heeg, B. M. S. (2021) · Value in Health · doi:10.1016/j.jval.2021.03.008 · Cited by 42
Zhu, A., Matoba, N., Wilson, E., Tapia, A. L., Li, Y., Ibrahim, J. G., Stein, J. L., & Love, M. I. (2021) · PLoS Genetics · doi:10.1371/journal.pgen.1009455 · Cited by 32
“MRLocus consists of two steps, (1) colocalization and (2) MR slope fitting, each of which use Bayesian hierarchical models specified in the Stan probabilistic programming language, and with posterior inference using the Stan and RStan software packages [31].”
MethodTrouvé, R., Oborne, L., & Baker, P. J. (2021) · Ecological Applications · doi:10.1002/eap.2383 · Cited by 41
Matsuyama, T., Tu, H., Sun, J., et al. (2021) · iScience · doi:10.1016/j.isci.2021.102866 · Cited by 41
Fitting Multilevel Vector Autoregressive Models in Stan, JAGS, and Mplus
Li, Y., Wood, J., Ji, L., Chow, S., & Oravecz, Z. (2021) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2021.1911657 · Cited by 44
Boosting Variational InferencePreprint
Guo, F., Wang, X., Fan, K., Broderick, T., & Dunson, D. B. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1611.05559 · Cited by 41
“T. Zhang.”
BackgroundMethodLambert, B. C., Kontonatsios, G., Mauch, M., Kokkoris, T., Jockers, M. L., Ananiadou, S., & Leroi, A. M. (2020) · Nature Human Behaviour · doi:10.1038/s41562-019-0802-4 · Cited by 42
Chan, X. H. S., Win, Y. N., Haeusler, I. L., Tan, J. Y., Loganathan, S., Saralamba, S., Chan, S. K. S., Ashley, E. A., Barnes, K. I., Baiden, R., et al. (2020) · PLoS Medicine · doi:10.1371/journal.pmed.1003040 · Cited by 42
“Once digi- tised, individual patient-level data sets were converted into a standard file format using Stat/ Transfer [13] version 13.3, then standardised and checked according to a prespecified data dictionary (Data Standardisation in S1 Appendix).”
BackgroundInfluentialGrahek, I., Frömer, R., Fahey, M. P., & Shenhav, A. (2022) · Cerebral Cortex · doi:10.1093/cercor/bhac215 · Cited by 40
Brieant, A. E., Vannucci, A., Nakua, H., Harris, J., Lovell, J. R., brundavanam, D., Tottenham, N., & Gee, D. G. (2023) · Developmental Cognitive Neuroscience · doi:10.1016/j.dcn.2023.101256 · Cited by 49
Kuehn, N. M., Bozorgnia, Y., Campbell, K. W., et al. (2023) · Earthquake Spectra · doi:10.1177/87552930231180906 · Cited by 40
Merging MCMC Subposteriors through Gaussian-Process Approximations
Nemeth, C., & Sherlock, C. (2017) · Bayesian Analysis · doi:10.1214/17-ba1063 · Cited by 40
“The STAN modelling language automatically tunes the HMC algorithm, and by using efficient automatic differentiaion, the user need only express their posterior model.”
MethodInfluentialZero-inflated hierarchical models for faecal egg counts to assess anthelmintic efficacy
Wang, C., Torgerson, P. R., Höglund, J., & Furrer, R. (2016) · Veterinary Parasitology · doi:10.1016/j.vetpar.2016.12.007 · Cited by 40
“1-1 (Wang and Paul, 2016) using the modelling language Stan (Carpenter, 2015), Stan uses an effective MCMC sampling technique and is available through the “stan” package (Guo et al.”
MethodInfluentialA Probabilistic Programming Approach for Outlier Detection in Healthcare Claims
Bauder, R. A., & Khoshgoftaar, T. M. (2016) · International Conference on Machine Learning and Applications · doi:10.1109/icmla.2016.0063 · Cited by 41
“Additionally, the use of Grubbs’ test to find acceptable utilization deviations assumes normality, which may not be applicable to some datasets requiring data transformation or using a different test for outliers [5].”
MethodMalware in the future? Forecasting of analyst detection of cyber events
Bakdash, J. Z., Hutchinson, S. E., Zaroukian, E. G., Marusich, L. R., Thirumuruganathan, S., Sample, C., Hoffman, B., & Das, G. (2018) · Journal of Cybersecurity · doi:10.1093/cybsec/tyy007 · Cited by 45
“The BSSM was implemented in the statistical programming language R using the brms package [36] as a wrapper for the probabilistic programming language Stan [37].”
MethodCarlisi, C. O., Norman, L. J., Murphy, C. M., Christakou, A., Chantiluke, K. C., Giampietro, V., Simmons, A., Brammer, M. J., Murphy, D., Mataix‐Cols, D., et al. (2017) · Cerebral Cortex · doi:10.1093/cercor/bhx265 · Cited by 44
“0 (Carpenter et al. 2017)) uses a specific probabilistic sampler called Hamiltonian Monte Carlo (HMC) to sample from the posterior distribution.”
InfluentialMoreno‐Torres, I., González‐García, C., Marconi, M., García‐Grande, A., Rodríguez‐Esparragoza, L., Elvira, V., Ramil, E., Campos-Ruíz, L., García-Hernández, R., Al‐Shahrour, F., et al. (2018) · Frontiers in Immunology · doi:10.3389/fimmu.2018.01693 · Cited by 41
“The model was fitted with the rstanarm package (13).”
MethodEshaghi, A., Kievit, R., Prados, F., Sudre, C. H., Nicholas, J. M., Cardoso, M. J., Chan, D., Nicholas, R. S., Sebastien Ourselin, A., Greenwood, J., et al. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1818978116 · Cited by 36
Orienting to polarized light at night—matching lunar skylight to performance in a nocturnal beetle
Foster, J. J., Kirwan, J. D., el Jundi, B., Smolka, J., Khaldy, L., Baird, E., Byrne, M. J., Nilsson, D.-E., Johnsen, S., & Dacke, M. (2018) · Journal of Experimental Biology · doi:10.1242/jeb.188532 · Cited by 40
“A Bayesian generalized linear model was implemented in the Stan language (Carpenter et al., 2017), using the package brms 2.”
MethodGaiser, R. A., Pessia, A., Ateeb, Z., Davanian, H., Moro, C. F., Alkharaan, H., Healy, K., Ghazi, S. H., Arnelo, U., Valente, R., et al. (2019) · Scientific Reports · doi:10.1038/s41598-019-46634-6 · Cited by 39
Neogi, S., Hoy, M., Dang, K., Yu, H., & Dauwels, J. (2020) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2020.2995166 · Cited by 40
“We trained FLDCRF 6 model parameters with Stan’s [31] in-built BFGS optimizer.”
MethodBenredjem, B., Gallion, J. M., Pelletier, D. J., Dallaire, P., Charbonneau, J., Cawkill, D., Nagi, K., Gosink, M. M., Lukasheva, V., Jenkinson, S. G., et al. (2019) · Nature Communications · doi:10.1038/s41467-019-11875-6 · Cited by 40
Model-based pre-election polling for national and sub-national outcomes in the US and UK
Lauderdale, B. E., Bailey, D., Blumenau, J., & Rivers, D. (2019) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2019.05.012 · Cited by 40
“2016 EU Referendum 2016 US Presidential Election 2017 UK General Election I – GE2015 vote [7] I – 2012 vote [5] I – GE15 vote [9] I – Quali cations [6] I – Quali cations [5] I – Quali cations [8] I – Age [14] I – Age [15] I – Age [14] I – Gender [2] I – Gender [2] I – Gender [2] I – Days ago [14] I – Days ago [14] I –…”
InfluentialLemoine, É., Dallaire, F., Yadav, R., Agarwal, R., Kadoury, S., Trudel, D., Guiot, M., Petrecca, K., & Leblond, F. (2019) · The Analyst · doi:10.1039/c9an01144g · Cited by 41
Implicitly adaptive importance sampling
Paananen, T., Piironen, J., Bürkner, P., & Vehtari, A. (2021) · Statistics and Computing · doi:10.1007/s11222-020-09982-2 · Cited by 43
“We also provide convenience functions that implement the moment matching method for models fitted with probabilistic programming language Stan (Carpenter et al. 2017).”
MethodInfluentialA Bayesian approach for predicting food and beverage sales in staff canteens and restaurants
Posch, K., Truden, C., Hungerländer, P., & Pilz, J. (2021) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2021.06.001 · Cited by 40
“We have implemented the models proposed in Section 4 using RStan [36], the interface between the programming languages R [32] and Stan [6].”
MethodInfluentialGradients Do Grow on Trees: A Linear-Time O ( N )-Dimensional Gradient for Statistical Phylogenetics
Ji, X., Zhang, Z., Holbrook, A. J., Nishimura, A., Baele, G., Rambaut, A., Lemey, P., & Suchard, M. A. (2020) · Molecular Biology and Evolution · doi:10.1093/molbev/msaa130 · Cited by 41
“sampling efficiency of HMC in many situations (Salvatier et al. 2016; Carpenter et al. 2017).”
BackgroundInfluential
Metadata
- Authors
- Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., & Riddell, A.
- Affiliations
- Columbia University (US)
- Adobe Systems (United States) (US)
- York University (CA)
- Indiana University (US)
- ORCID
- Venue
- Journal of Statistical Software
- Publisher
- Foundation for Open Access Statistic
- Published
- 2017
- Volume
- 76
- Issue
- 1
- Pages
- 1-32
- ISSN
- 1548-7660 (ISSN-L)
- PMC
- PMC9788645
- OpenAlex
- W2577537660
- Semantic Scholar
- f8110d834fcc9a3a1c4416d4b165984219fe26f4
- Cited by
- 7,754
- References
- 49
- Citations by year
- 2026: 672 · 2025: 811 · 2024: 811 · 2023: 835 · 2022: 917 · 2021: 1127 · 2020: 970 · 2019: 752 · 2018: 516 · 2017: 253
- FWCI
- 474.30
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by
- Locations
- Journal of Statistical Software (publishedVersion, cc-by)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Journal of Systems and Software
- Grantee Submission
- Funders
- National Science Foundation (0934516, 1205516)
- U.S. Department of Energy (DESC0002099)
- Harvard University
- National Institutes of Health (1g20rr030893-01)
- Institute of Education Sciences (R305D090006-09A, R305D090006)
- National Center for Research Resources (G20RR030893)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Mathematics › Statistics and Probability › Data Analysis with R
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- Stan, probabilistic programming languages, Bayesian inference, Markov chain Monte Carlo, No-U-Turn Sampler, Hamiltonian Monte Carlo, L-BFGS optimization, penalized likelihood, variational inference, expectation propagation, marginal inference, R interface, Python interface, posterior analysis
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.
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