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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Citations
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BackgroundInfluentialRiemann manifold langevin and hamiltonian monte carlo methods
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Carpenter, B., Hoffman, M. D., Brubaker, M. A., Lee, D. D., Li, P., & Betancourt, M. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1509.07164 · Cited by 68
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MethodGeneralizing the No-U-Turn Sampler to Riemannian ManifoldsPreprint
Betancourt, M. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1304.1920 · Cited by 32 · cited 3×
“Riemannian manifold Hamiltonian Monte Carlo (RHMC) introduces a location-dependent metric that can overcome these final hurdles (Girolami and Calderhead 2011); Stan has a prototype implementation of RHMC based on the SoftAbs metric of (Betancourt 2012), using a generalization of NUTS to Riemannian manifolds (Betancour…”
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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
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“Possibly the most powerful program for performing full Bayesian inference available to date is Stan (Stan Development Team, 2017b; Carpenter et al., 2017).”
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“…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
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Global estimates of mortality associated with long-term exposure to outdoor fine particulate matter
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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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