Stan (software)

Stan

Original author(s)	Stan Development Team
Initial release	August 30, 2012
Stable release	2.13.0 / November 25, 2016
Repository	github.com/stan-dev/stan
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
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]: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

Interfaces

Stan can be accessed through several interfaces:

• CmdStan - command-line executable for the shell
• RStan - integration with the R software environment
• 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

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]:3, 26[2]:28} (NUTS), a variant of HMC and Stan's default MCMC engine
  • Hamiltonian Monte Carlo
• Variational inference algorithms:
  • Black-box Variational Inference^[3]
• 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]:199 The automatic differentiation within Stan can be used outside of the probabilistic programming language.

Usage

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

References

1. 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:1506.03431.
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

• Carpenter, Bob, Andrew Gelman, Matt Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. Stan: A probabilistic programming language, Journal of Statistical Software.
• 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, Proceedings of the NIPS Workshop on Probabilistic Programming.

External links

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