Stan (software)

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Original author(s) Stan Development Team
Initial release August 30, 2012 (2012-08-30)
Stable release
2.14.0 / December 26, 2016 (2016-12-26)
Development status Active
Written in C++
Operating system Unix-like, Microsoft Windows, Mac OS X
Platform Intel x86 - 32-bit, x64
Size 41.2 MB
Type Statistical package
License New BSD License

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]:2

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


Stan can be accessed through several interfaces:


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[edit]

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]:199 The automatic differentiation within Stan can be used outside of the probabilistic programming language.


Stan is used in fields including social science[4] and pharmaceutical statistics.[5]


  1. ^ a b c d e Stan Development Team. 2015. Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0
  2. ^ 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. 
  3. ^ Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. (June 2015). "Automatic Variational Inference in Stan". 1506.03431. arXiv:1506.03431Freely accessible. 
  4. ^ 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
  5. ^ 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. 

Further reading[edit]

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