Stan (software)

For other uses, see Stan (disambiguation).

Stan

Original author(s)	Stan Development Team
Initial release	August 30, 2012 (2012-08-30)
Stable release	2.36.0 [1]   / 10 December 2024;5 months ago (10 December 2024)
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++. ^[2] The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function. ^[2]

Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the Monte Carlo method. ^[2]

Stan was created by a development team consisting of 52 members ^[3] that includes Andrew Gelman, Bob Carpenter, Daniel Lee, Ben Goodrich, and others.

Example

A simple linear regression model can be described as ${\displaystyle y_{n}=\alpha +\beta x_{n}+\epsilon _{n}}$, where ${\displaystyle \epsilon _{n}\sim {\text{normal}}(0,\sigma )}$. This can also be expressed as ${\displaystyle y_{n}\sim {\text{normal}}(\alpha +\beta X_{n},\sigma )}$. The latter form can be written in Stan as the following:

data{int<lower=0>N;vector[N]x;vector[N]y;}parameters{realalpha;realbeta;real<lower=0>sigma;}model{y~normal(alpha+beta*x,sigma);}

Interfaces

The Stan language itself can be accessed through several interfaces:

• CmdStan – a command-line executable for the shell,
• CmdStanR and rstan – R software libraries,
• CmdStanPy and PyStan – libraries for the Python programming language,
• CmdStan.rb - library for the Ruby programming language,
• MatlabStan – integration with the MATLAB numerical computing environment,
• Stan.jl – integration with the Julia programming language,
• StataStan – integration with Stata.
• Stan Playground - online at

In addition, higher-level interfaces are provided with packages using Stan as backend, primarily in the R language: ^[4]

• rstanarm provides a drop-in replacement for frequentist models provided by base R and lme4 using the R formula syntax;
• brms ^[5] provides a wide array of linear and nonlinear models using the R formula syntax;
• prophet provides automated procedures for 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:
  • Hamiltonian Monte Carlo (HMC)
  • No-U-Turn sampler ^{[2] [6]} (NUTS), a variant of HMC and Stan's default MCMC engine
• Variational inference algorithms:
  • Automatic Differentiation Variational Inference ^[7]
  • Pathfinder: Parallel quasi-Newton variational inference ^[8]
• Optimization algorithms:
  • Limited-memory BFGS (L-BFGS) (Stan's default optimization algorithm)
  • Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS)
  • Laplace's approximation 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. ^[2] The automatic differentiation within Stan can be used outside of the probabilistic programming language.

Usage

Stan is used in fields including social science, ^[9] pharmaceutical statistics, ^[10] market research, ^[11] and medical imaging. ^[12]

See also

• PyMC is a probabilistic programming language in Python
• ArviZ a Python library for Exploratory Analysis of Bayesian Models

References

1. "Release 2.36.0". 10 December 2024. Retrieved 30 December 2024.
2. Stan Development Team. 2015. Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0
3. "Development Team". stan-dev.github.io. Retrieved 2024-11-21.
4. Gabry, Jonah. "The current state of the Stan ecosystem in R". Statistical Modeling, Causal Inference, and Social Science. Retrieved 25 August 2020.
5. "BRMS: Bayesian Regression Models using 'Stan'". 23 August 2021.
6. 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.
7. Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. (June 2015). "Automatic Variational Inference in Stan". 1506 (3431). arXiv: 1506.03431 . Bibcode:2015arXiv150603431K.{{cite journal}}: Cite journal requires |journal= (help)
8. Zhang, Lu; Carpenter, Bob; Gelman, Andrew; Vehtari, Aki (2022). "Pathfinder: Parallel quasi-Newton variational inference". Journal of Machine Learning Research . 23 (306): 1–49.
9. 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
10. 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. S2CID   19738522.
11. Feit, Elea (15 May 2017). "Using Stan to Estimate Hierarchical Bayes Models" . Retrieved 19 March 2019.
12. 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 . Bibcode:2019JBO....24l6004G. doi:10.1117/1.JBO.24.12.126004. PMC   7006047 . PMID   31840442.

Further reading

• Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew; Lee, Daniel; Goodrich, Ben; Betancourt, Michael; Brubaker, Marcus; Guo, Jiqiang; Li, Peter; Riddell, Allen (2017). "Stan: A Probabilistic Programming Language". Journal of Statistical Software. 76 (1): 1–32. doi: 10.18637/jss.v076.i01 . ISSN   1548-7660. PMC   9788645 . PMID   36568334.
• Gelman, Andrew, Daniel Lee, and Jiqiang Guo (2015). Stan: A probabilistic programming language for Bayesian inference and optimization, Journal of Educational and Behavioral Statistics.
• Hoffman, Matthew D., Bob Carpenter, and Andrew Gelman (2012). Stan, scalable software for Bayesian modeling Archived 2015-01-21 at the Wayback Machine , Proceedings of the NIPS Workshop on Probabilistic Programming.

External links

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