The DOI matches its Crossref record; 44 of the 49 references it cites were found in a registry or an index.
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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Cites
R: A Language and Environment for Statistical Computing
R Core Team (2000) · doi:10.32614/r.manuals · Cited by 355,893
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003) · doi:10.1201/9780429258480 · Cited by 27,276 · cited 8×
“This supplies fairly diffuse starting points when transformed back to the constrained scale, and thus help with convergence diagnostics as discussed in (Gelman et al. 2013).”
BackgroundMethodInfluentialSelf-citationInference from iterative simulation using multiple sequences
Gelman, A., & Rubin, D. B. (1992) · Statistical Science · doi:10.1214/ss/1177011136 · Cited by 16,627 · cited 2×
“Before performing output analysis, we recommend generating multiple independent chains in order to more effectively monitor convergence; see (Gelman and Rubin 1992) for more analysis.”
MethodSelf-citationBraun, W. J., & Murdoch, D. J. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108993456.011 · Cited by 14,099
Data Analysis Using Regression and Multilevel/Hierarchical Models
Gelman, A., & Hill, J. (2006) · doi:10.1017/cbo9780511790942 · Cited by 13,597
Self-citationNocedal, J. M., & Wright, S. J. (2006) · Springer series in operations research/Springer series in operations research and financial engineering · doi:10.1007/978-0-387-40065-5 · Cited by 10,206
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 · cited 3×
“(Gelman et al. 2013, Section 5.1) define a hierarchical model of the incidence of tumors in rats in control groups across trials; a very similiar model is defined for mortality rates in pediatric surgeries across hospitals in (Lunn et al. 2000, 2009, Examples, Volume 1).”
BackgroundMethodInfluentialJAGS: A program for analysis of Bayesian graphical models using Gibbs sampling
Plummer, M. (2003) · Cited by 4,720
Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)91197-x · Cited by 4,081
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brms : An R Package for Bayesian Multilevel Models Using Stan
Bürkner, P.-C. (2017) · Journal of Statistical Software · doi:10.18637/jss.v080.i01 · Cited by 9,476
“Similar to software packages like WinBugs , Stan comes with its own programming language, allowing for great modeling Ćexibility (cf., Stan Development Team 2017b; Carpenter et al. 2017).”
BackgroundMethodAdvanced Bayesian Multilevel Modeling with the R Package brms
Bürkner, P.-C. (2018) · The R Journal · doi:10.32614/rj-2018-017 · Cited by 3,015
“Possibly the most powerful program for performing full Bayesian inference available to date is Stan (Stan Development Team, 2017b; Carpenter et al., 2017).”
BackgroundTaylor, S. J., & Letham, B. (2017) · The American Statistician · doi:10.1080/00031305.2017.1380080 · Cited by 2,904
“…sum of each of these components, plus noise: When the seasonality and holiday features for each observation are combined into a matrix X and the changepoint indicators a ( t ) in a matrix A , the entire model can be expressed in a few lines of Stan code [Carpenter et al., 2016], given in Listing 1.”
dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences
Speagle, J. S. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa278 · Cited by 2,697
Global estimates of mortality associated with long-term exposure to outdoor fine particulate matter
Burnett, R., Chen, H., Szyszkowicz, M., Fann, N., Hubbell, B., Pope, C. A., Apte, J. S., Brauer, M., Cohen, A., Weichenthal, S., et al. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1803222115 · Cited by 2,504
“US Environmental Protection Agency (2012) Regulatory impact analysis for the final revisions to the national ambient air quality standards for particulate matter (Office of Air Quality Planning and Standards, Health and Environmental Impacts Division, Research Triangle Park, NC), Technical Report EPA-452/R-12-005.”
MethodInfluential
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
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