Stan is a probabilistic programming language for statistical inference written in C++.Stan Development Team. 2015
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 A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, ...

with an

imperative program In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program ...

calculating the log

probability density function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) c ...

. Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the

Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...

. Stan was created by a development team consisting of 34 members that includes Andrew Gelman, Bob Carpenter, Matt Hoffman, and Daniel Lee.

Interfaces

The Stan language itself can be accessed through several interfaces: * CmdStan – a command-line executable for the shell, * CmdStanR and rstan – R software libraries, * CmdStanPy and PyStan – libraries for the Python programming language, * MatlabStan – integration with the

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...

numerical computing environment, * Stan.jl – integration with the

Julia programming language Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic progr ...

, * StataStan – integration with Stata. In addition, higher-level interfaces are provided with packages using Stan as backend, primarily in the R language: * ''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; * ''prophet'' provides automated procedures for

time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. E ...

forecasting.

Algorithms

Stan implements gradient-based

Markov chain Monte Carlo In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain ...

(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: ** Hamiltonian Monte Carlo (HMC) ** No-U-Turn sampler (NUTS), a variant of HMC and Stan's default MCMC engine * Variational inference algorithms: ** Automatic Differentiation Variational Inference * Optimization algorithms: ** Limited-memory BFGS (Stan's default optimization algorithm) **

Broyden–Fletcher–Goldfarb–Shanno algorithm In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines th ...

Laplace's method In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form :\int_a^b e^ \, dx, where f(x) is a twice- differentiable function, ''M'' is a large number, and the endpoints ''a'' ...

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

Usage

Stan is used in fields including social science,

pharmaceutical statistics ''Pharmaceutical Statistics'' is a peer-reviewed scientific journal that publishes papers related to pharmaceutical statistics. It is the official journal of Statisticians in the Pharmaceutical Industry and is published by John Wiley & Sons. Abst ...

market research Market research is an organized effort to gather information about target markets and customers: know about them, starting with who they are. It is an important component of business strategy and a major factor in maintaining competitiveness. Ma ...

, and medical imaging.

References

External links

Stan web site

Stan source
a Git repository hosted on

GitHub GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, co ...

{{Statistical software Computational statistics Free Bayesian statistics software Monte Carlo software Numerical programming languages Domain-specific programming languages Probabilistic software