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]
Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the Monte Carlo method.[1]
Stan was created by a development team consisting of 34 members[2] that includes Andrew Gelman, Bob Carpenter, Matt Hoffman, and Daniel Lee.
Interfaces
The Stan language itself can be accessed through several interfaces:
CmdStan - command-line executable for the shell
RStan - integration with the R software environment, maintained by Andrew Gelman and colleagues
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
In addition, higher-level interfaces are provided with packages using Stan as backend, primarily in the R language[3]:
rstanarm - provides a drop-in replacement for frequentist models provided by base R and lme4 using the R formula syntax
brms - provides a wide array of linear and nonlinear models using the R formula syntax [4]
blavaan - provides latent variable models, including confirmatory factor analysis, structural equation models, and latent growth curve models
prophet - provides 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:
No-U-Turn sampler[1][5] (NUTS), a variant of HMC and Stan's default MCMC engine
Hamiltonian Monte Carlo
Variational inference algorithms:
Black-box Variational Inference[6]
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] The automatic differentiation within Stan can be used outside of the probabilistic programming language.
Usage
Stan is used in fields including social science,[7] pharmaceutical statistics,[8] market research,[9] and medical imaging.[10]
References
Stan Development Team. 2015. Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0
"Development Team". stan-dev.github.io. Retrieved 2018-07-25.
Gabry, Jonah. "The current state of the Stan ecosystem in R". Statistical Modeling, Causal Inference, and Social Science. Retrieved 25 August 2020.
https://cran.r-project.org/web/packages/brms/index.html
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.
Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. (June 2015). "Automatic Variational Inference in Stan". 1506 (3431). arXiv:1506.03431. Bibcode:2015arXiv150603431K.
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
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.
Feit, Elea. "Using Stan to Estimate Hierarchical Bayes Models". Retrieved 19 March 2019.
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 (2018). "Quantitative phase and polarisation endoscopy applied to detection of early oesophageal tumourigenesis". arXiv:1811.03977 [physics.med-ph].
Further reading
Bob, Carpenter; Andrew, Gelman; Matthew, Hoffman; Daniel, Lee; Ben, Goodrich; Michael, Betancourt; Marcus, Brubaker; Jiqiang, Guo; Peter, Li; Allen, Riddell (2017). "Stan: A Probabilistic Programming Language". Journal of Statistical Software. 76 (1): 1–32. doi:10.18637/jss.v076.i01. ISSN 1548-7660.
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
Statistical software
Public domain
Dataplot Epi Info CSPro X-12-ARIMA
Open-source
ADMB DAP gretl JASP JAGS JMulTi Julia GNU Octave OpenBUGS Orange PSPP PyMC3 R (RStudio) SageMath SimFiT SOFA Statistics Stan XLispStat
Freeware
BV4.1 CumFreq SegReg XploRe WinBUGS
Commercial
Cross-platform
Data Desk GAUSS GraphPad InStat GraphPad Prism IBM SPSS Statistics IBM SPSS Modeler JMP Maple Mathcad Mathematica MATLAB OxMetrics RATS Revolution Analytics SAS SmartPLS Stata StatView SUDAAN S-PLUS TSP World Programming System (WPS)
Windows only
BMDP EViews GenStat LIMDEP LISREL MedCalc Microfit Minitab MLwiN NCSS SHAZAM SigmaStat Statistica StatsDirect StatXact SYSTAT The Unscrambler UNISTAT
Excel add-ons
Analyse-it SigmaXL UNISTAT for Excel XLfit RExcel
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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