Stan (software)

Stan
Original author(s)	Stan Development Team
Initial release	August 30, 2012
Stable release	2.24 / August 2020
Repository	github.com/stan-dev/stan ;
Written in	C++
Operating system	Unix-like, Microsoft Windows, Mac OS X
Platform	Intel x86 - 32-bit, x64
Type	Statistical package
License	New BSD License
Website	mc-stan.org

Stan is a probabilistic programming language for statistical inference written in C++.^[1] The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function.^[1]

Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the Monte Carlo method.^[1]

Stan was created by a development team consisting of 34 members^[2] that includes Andrew Gelman, Bob Carpenter, Matt Hoffman, and Daniel Lee.

Interfaces[]

The Stan language itself can be accessed through several interfaces:

CmdStan - command-line executable for the shell
RStan - integration with the R software environment, maintained by Andrew Gelman and colleagues
PyStan - integration with the Python programming language
MatlabStan - integration with the MATLAB numerical computing environment
Stan.jl - integration with the Julia programming language
StataStan - integration with Stata

In addition, higher-level interfaces are provided with packages using Stan as backend, primarily in the R language:^[3]

rstanarm - provides a drop-in replacement for frequentist models provided by base R and lme4 using the R formula syntax
brms - provides a wide array of linear and nonlinear models using the R formula syntax ^[4]
blavaan - provides latent variable models, including confirmatory factor analysis, structural equation models, and latent growth curve models
prophet - provides time series forecasting

Algorithms[]

Stan implements gradient-based Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference, stochastic, gradient-based variational Bayesian methods for approximate Bayesian inference, and gradient-based optimization for penalized maximum likelihood estimation.

MCMC algorithms:
- No-U-Turn sampler^[1]^[5] (NUTS), a variant of HMC and Stan's default MCMC engine
- Hamiltonian Monte Carlo (HMC)
Variational inference algorithms:
- Black-box Variational Inference^[6]
Optimization algorithms:
- Limited-memory BFGS (Stan's default optimization algorithm)
- Broyden–Fletcher–Goldfarb–Shanno algorithm
- Laplace's method for classical standard error estimates and approximate Bayesian posteriors

Automatic differentiation[]

Stan implements reverse-mode automatic differentiation to calculate gradients of the model, which is required by HMC, NUTS, L-BFGS, BFGS, and variational inference.^[1] The automatic differentiation within Stan can be used outside of the probabilistic programming language.

Usage[]

Stan is used in fields including social science,^[7] pharmaceutical statistics,^[8] market research,^[9] and medical imaging.^[10]

References[]

^ ^a ^b ^c ^d ^e Stan Development Team. 2015. Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0
^ "Development Team". stan-dev.github.io. Retrieved 2018-07-25.
^ Gabry, Jonah. "The current state of the Stan ecosystem in R". Statistical Modeling, Causal Inference, and Social Science. Retrieved 25 August 2020.
^ "BRMS: Bayesian Regression Models using 'Stan'". 23 August 2021.
^ Hoffman, Matthew D.; Gelman, Andrew (April 2014). "The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo". Journal of Machine Learning Research. 15: pp. 1593–1623.
^ Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. (June 2015). "Automatic Variational Inference in Stan". 1506 (3431). arXiv:1506.03431. Bibcode:2015arXiv150603431K. Cite journal requires |journal= (help)
^ Goodrich, Benjamin King, Wawro, Gregory and Katznelson, Ira, Designing Quantitative Historical Social Inquiry: An Introduction to Stan (2012). APSA 2012 Annual Meeting Paper. Available at SSRN 2105531
^ Natanegara, Fanni; Neuenschwander, Beat; Seaman, John W.; Kinnersley, Nelson; Heilmann, Cory R.; Ohlssen, David; Rochester, George (2013). "The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group". Pharmaceutical Statistics. 13 (1): 3–12. doi:10.1002/pst.1595. ISSN 1539-1612. PMID 24027093.
^ Feit, Elea (15 May 2017). "Using Stan to Estimate Hierarchical Bayes Models". Retrieved 19 March 2019.
^ Gordon, GSD; Joseph, J; Alcolea, MP; Sawyer, T; Macfaden, AJ; Williams, C; Fitzpatrick, CRM; Jones, PH; di Pietro, M; Fitzgerald, RC; Wilkinson, TD; Bohndiek, SE (2019). "Quantitative phase and polarization imaging through an optical fiber applied to detection of early esophageal tumorigenesis". Journal of Biomedical Optics. 24 (12): 1–13. arXiv:1811.03977. doi:10.1117/1.JBO.24.12.126004. PMC 7006047. PMID 31840442.

External links[]

Stan web site
Stan source, a Git repository hosted on GitHub

[Stan2015-1] Stan Development Team. 2015. Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0

[2] "Development Team". stan-dev.github.io. Retrieved 2018-07-25.

[3] Gabry, Jonah. "The current state of the Stan ecosystem in R". Statistical Modeling, Causal Inference, and Social Science. Retrieved 25 August 2020.

[4] "BRMS: Bayesian Regression Models using 'Stan'". 23 August 2021.

[NUTS2014-5] Hoffman, Matthew D.; Gelman, Andrew (April 2014). "The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo". Journal of Machine Learning Research. 15: pp. 1593–1623.

[kucukelbir20153-6] Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. (June 2015). "Automatic Variational Inference in Stan". 1506 (3431). arXiv:1506.03431. Bibcode:2015arXiv150603431K. Cite journal requires |journal= (help)

[7] Goodrich, Benjamin King, Wawro, Gregory and Katznelson, Ira, Designing Quantitative Historical Social Inquiry: An Introduction to Stan (2012). APSA 2012 Annual Meeting Paper. Available at SSRN 2105531

[8] Natanegara, Fanni; Neuenschwander, Beat; Seaman, John W.; Kinnersley, Nelson; Heilmann, Cory R.; Ohlssen, David; Rochester, George (2013). "The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group". Pharmaceutical Statistics. 13 (1): 3–12. doi:10.1002/pst.1595. ISSN 1539-1612. PMID 24027093.

[9] Feit, Elea (15 May 2017). "Using Stan to Estimate Hierarchical Bayes Models". Retrieved 19 March 2019.

[pmid27279676-10] Gordon, GSD; Joseph, J; Alcolea, MP; Sawyer, T; Macfaden, AJ; Williams, C; Fitzpatrick, CRM; Jones, PH; di Pietro, M; Fitzgerald, RC; Wilkinson, TD; Bohndiek, SE (2019). "Quantitative phase and polarization imaging through an optical fiber applied to detection of early esophageal tumorigenesis". Journal of Biomedical Optics. 24 (12): 1–13. arXiv:1811.03977. doi:10.1117/1.JBO.24.12.126004. PMC 7006047. PMID 31840442.

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