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Stan (software)

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Stan
Original author(s)Stan Development Team
Initial releaseAugust 30, 2012 (2012-08-30)
Stable release
2.35.0[1] Edit this on Wikidata / 3 June 2024; 3 months ago (3 June 2024)
Repository
Written inC++
Operating systemUnix-like, Microsoft Windows, Mac OS X
PlatformIntel x86 - 32-bit, x64
TypeStatistical package
LicenseNew BSD License
Websitemc-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 34 members[3] that includes Andrew Gelman, Bob Carpenter, Matt Hoffman, and Daniel Lee.

Example

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A simple linear regression model can be described as , where . This can also be expressed as . The latter form can be written in Stan as the following:

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

Interfaces

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The Stan language itself can be accessed through several interfaces:

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

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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.

Automatic differentiation

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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

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Stan is used in fields including social science,[8] pharmaceutical statistics,[9] market research,[10] and medical imaging.[11]

See also

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

References

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  1. ^ "Release 2.35.0". 3 June 2024. Retrieved 26 June 2024.
  2. ^ a b c d e 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 2018-07-25.
  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. ^ 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
  9. ^ 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.
  10. ^ Feit, Elea (15 May 2017). "Using Stan to Estimate Hierarchical Bayes Models". Retrieved 19 March 2019.
  11. ^ 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

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