Stan (software)
Probabilistic programming language for Bayesian inference From Wikipedia, the free encyclopedia
Stan is a probabilistic programming language for statistical inference written in C++.[2] The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function.[2]
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Original author(s) | Stan Development Team |
---|---|
Initial release | August 30, 2012 |
Stable release | |
Repository | |
Written in | C++ |
Operating system | Unix-like, Microsoft Windows, Mac OS X |
Platform | Intel x86 - 32-bit, x64 |
Type | Statistical package |
License | New BSD License |
Website | mc-stan |
Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the Monte Carlo method.[2]
Stan was created by a development team consisting of 52 members[3] that includes Andrew Gelman, Bob Carpenter, Daniel Lee, Ben Goodrich, and others.
Example
A simple linear regression model can be described as , where . This can also be expressed as . The latter form can be written in Stan as the following:
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);
}
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,
- CmdStan.rb - library for the 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
In addition, higher-level interfaces are provided with packages using Stan as backend, primarily in the R language:[4]
- rstanarm provides a drop-in replacement for frequentist models provided by base R and lme4 using the R formula syntax;
- brms[5] 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 for penalized maximum likelihood estimation.
- MCMC algorithms:
- Hamiltonian Monte Carlo (HMC)
- No-U-Turn sampler[2][6] (NUTS), a variant of HMC and Stan's default MCMC engine
- Variational inference algorithms:
- 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.[2] The automatic differentiation within Stan can be used outside of the probabilistic programming language.
Usage
Stan is used in fields including social science,[9] pharmaceutical statistics,[10] market research,[11] and medical imaging.[12]
See also
References
Further reading
External links
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