View source for Stan (software)

{{Short description|Probabilistic programming language for Bayesian inference}}
{{Other uses|Stan (disambiguation)}}
{{Infobox software
| name = Stan
| logo = Stan (programming) logo.png
| author = Stan Development Team
| released = {{Start date|2012|8|30}}
| discontinued = 
| latest release version = {{wikidata|property|edit|reference|P348}}
| latest release date    = {{start date and age|{{wikidata|qualifier|P348|P577}}}}
| programming language = [[C++]]
| operating system = [[Unix-like]], [[Microsoft Windows]], [[Mac OS X]]
| platform = [[IA-32|Intel x86 - 32-bit]], [[x86-64|x64]]
| genre = [[Statistical package]]
| license = [[BSD licenses#3-clause license ("Revised BSD License", "New BSD License", or "Modified BSD License")|New BSD License]]
| website = {{URL|https://mc-stan.org/}}
}}

'''Stan''' is a [[probabilistic programming language]] for [[statistical inference]] written in [[C++]].<ref name="Stan2015">Stan Development Team. 2015. [https://github.com/stan-dev/stan/releases/download/v2.9.0/stan-reference-2.9.0.pdf Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0]</ref> The Stan language is used to specify a (Bayesian) [[statistical model]] with an [[Imperative programming|imperative program]] calculating the log [[probability density function]].<ref name="Stan2015" />

Stan is licensed under the [[BSD licenses#3-clause license ("Revised BSD License", "New BSD License", or "Modified BSD License")|New BSD License]]. Stan is named in honour of [[Stanislaw Ulam]], pioneer of the [[Monte Carlo method]].<ref name="Stan2015" />

Stan was created by a development team consisting of 52 members<ref>{{Cite news|url=http://mc-stan.org/about/team/|title=Development Team|work=stan-dev.github.io|access-date=2024-11-21|language=en-US}}</ref> that includes [[Andrew Gelman]], Bob Carpenter, Daniel Lee, Ben Goodrich, and others.

== Example ==
A simple linear regression model can be described as <math>y_n = \alpha + \beta x_n + \epsilon_n</math>, where <math>\epsilon_n \sim \text{normal} (0, \sigma)</math>. This can also be expressed as <math>y_n \sim \text{normal}(\alpha + \beta X_n, \sigma)</math>. The latter form can be written in Stan as the following:

<syntaxhighlight lang="stan">
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);
}
</syntaxhighlight>

== Interfaces ==
The Stan language itself can be accessed through several interfaces:
* CmdStan – a command-line executable for the [[Unix Shell|shell]],
* CmdStanR and rstan – [[R (programming language)|R software]] libraries,
* CmdStanPy and PyStan – libraries for the [[Python programming language]],
* CmdStan.rb - library for the [[Ruby | 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 [https://stan-playground.flatironinstitute.org/]

In addition, higher-level interfaces are provided with packages using Stan as backend, primarily in the [[R (programming language)|R language]]:<ref>{{cite web |last1=Gabry |first1=Jonah |title=The current state of the Stan ecosystem in R |url=https://statmodeling.stat.columbia.edu/2018/04/24/current-state-stan-ecosystem-r/ |website=Statistical Modeling, Causal Inference, and Social Science |accessdate=25 August 2020 |ref=stanecosystem}}</ref>

* ''rstanarm'' provides a drop-in replacement for frequentist models provided by base R and ''lme4'' using the R formula syntax;
* ''brms''<ref>{{Cite web|url=https://cran.r-project.org/web/packages/brms/index.html|title = BRMS: Bayesian Regression Models using 'Stan'|date = 23 August 2021}}</ref> 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 (mathematics)|optimization]] for penalized maximum likelihood estimation. 
* MCMC algorithms:
** [[Hamiltonian Monte Carlo]] (HMC)
** No-U-Turn sampler<ref name="Stan2015" /><ref name="NUTS2014">{{cite journal
 | last1 = Hoffman | first1 = Matthew D.
 | last2 = Gelman |first2 = Andrew
 | title = The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
 | journal = [[Journal of Machine Learning Research]]
 |date=April 2014
 | volume = 15
 | pages = ''pp.'' 1593&ndash;1623
 | url = http://jmlr.org/papers/v15/hoffman14a.html
}}</ref> (NUTS), a variant of HMC and Stan's default MCMC engine
* Variational inference algorithms:
** Automatic Differentiation Variational Inference<ref name="kucukelbir20153">{{cite journal
 |last1 = Kucukelbir|first1 = Alp|last2 = Ranganath|first2 = Rajesh|last3 = Blei|first3 = David M.|title = Automatic Variational Inference in Stan|date = June 2015|volume = 1506|issue = 3431|arxiv = 1506.03431|bibcode = 2015arXiv150603431K}}</ref>
** Pathfinder: Parallel quasi-Newton variational inference<ref name="Zhang2022">{{cite journal | last1=Zhang | first1=Lu | last2=Carpenter | first2=Bob | last3=Gelman | first3=Andrew | last4=Vehtari | first4=Aki | year=2022 | title=Pathfinder: Parallel quasi-Newton variational inference | journal=[[Journal of Machine Learning Research]] | volume=23 | issue=306 | pages=1–49 }}
</ref>
* Optimization algorithms:
** [[Limited-memory BFGS]] (Stan's default optimization algorithm)
** [[Broyden–Fletcher–Goldfarb–Shanno algorithm]] 
** [[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.<ref name="Stan2015" /> The automatic differentiation within Stan can be used outside of the probabilistic programming language.

== Usage ==
Stan is used in fields including social science,<ref>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}}</ref> [[pharmaceutical statistics]],<ref>{{cite journal |last1=Natanegara|first1= Fanni |last2=Neuenschwander|first2= Beat |last3=Seaman|first3= John W. |last4=Kinnersley| first4=Nelson |last5=Heilmann| first5=Cory R. |last6=Ohlssen|first6=David |last7=Rochester|first7= George| title=The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group| journal=Pharmaceutical Statistics| issn=1539-1612| doi=10.1002/pst.1595|pmid= 24027093 | year=2013 |pages=3–12| volume=13 |issue=1|s2cid= 19738522 }}</ref> [[market research]],<ref>{{cite web |last1=Feit |first1=Elea |title=Using Stan to Estimate Hierarchical Bayes Models |date=15 May 2017 |url=https://discourse.mc-stan.org/t/tutorial-on-using-stan-in-marketing-research/554 |accessdate=19 March 2019}}</ref> and [[medical imaging]].<ref name=pmid27279676>{{cite journal | last1=Gordon | first1=GSD | first2=J |last2=Joseph | first3=MP | last3= Alcolea | first4=T | last4= Sawyer | first5=AJ | last5=Macfaden | first6=C | last6=Williams | first7=CRM | last7=Fitzpatrick | first8 = PH | last8 = Jones | first9 = M | last9 =  di Pietro | first10=RC | last10=Fitzgerald | first11=TD | last11= Wilkinson | first12 = SE | last12 = Bohndiek | title = Quantitative phase and polarization imaging through an optical fiber applied to detection of early esophageal tumorigenesis | journal=Journal of Biomedical Optics | arxiv=1811.03977 | year=2019 | volume=24 | issue=12 | pages=1–13 | doi=10.1117/1.JBO.24.12.126004 | pmid=31840442 | pmc=7006047 | bibcode=2019JBO....24l6004G }}</ref>

== See also ==
* [[PyMC]] is a probabilistic programming language in Python
* [[ArviZ]] a Python library for Exploratory Analysis of Bayesian Models

== References ==
{{reflist|30em}}

== Further reading ==
* {{cite journal | first1 = Bob| last1 = Carpenter|
	first2 = Andrew| last2 = Gelman|
	first3 = Matthew| last3 = Hoffman|
	first4 = Daniel| last4 = Lee|
	first5 = Ben| last5 = Goodrich|
	first6 = Michael| last6 = Betancourt|
	first7 = Marcus| last7 = Brubaker|
	first8 = Jiqiang| last8 = Guo|
	first9 = Peter| last9 = Li|
	first10 = Allen| last10 = Riddell|
	title = Stan: A Probabilistic Programming Language|
	journal = Journal of Statistical Software|
	volume = 76|
	number = 1|
	year = 2017|
	issn = 1548-7660|
	pages = 1–32|
	doi = 10.18637/jss.v076.i01| pmid = 36568334| pmc = 9788645|
	doi-access = free}}
* Gelman, Andrew, Daniel Lee, and Jiqiang Guo (2015).  [http://www.stat.columbia.edu/~gelman/research/published/stan_jebs_2.pdf 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). [http://probabilistic-programming.org/wiki/NIPS*2012_Workshop/Schedule#talk-hoffman Stan, scalable software for Bayesian modeling] {{Webarchive|url=https://web.archive.org/web/20150121055338/http://probabilistic-programming.org/wiki/NIPS*2012_Workshop/Schedule#talk-hoffman |date=2015-01-21 }}, Proceedings of the NIPS Workshop on Probabilistic Programming.

== External links ==
* [http://mc-stan.org/ Stan web site]
* [https://github.com/stan-dev/stan Stan source], a [[Git (software)|Git]] repository hosted on [[GitHub]]

{{Statistical software}}

[[Category:Computational statistics]]
[[Category:Free Bayesian statistics software]]
[[Category:Monte Carlo software]]
[[Category:Numerical programming languages]]
[[Category:Domain-specific programming languages]]
[[Category:Probabilistic software]]