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.

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.

The latter form can be written in Stan as the following: The Stan language itself can be accessed through several interfaces: In addition, higher-level interfaces are provided with packages using Stan as backend, primarily in the R language:[4] 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.

Stan implements reverse-mode automatic differentiation to calculate gradients of the model, which is required by HMC, NUTS, L-BFGS, BFGS, and variational inference.

Stan is used in fields including social science,[9] pharmaceutical statistics,[10] market research,[11] and medical imaging.