Stan has transformed the practice of Bayesian statistics by providing a high-performance, general-purpose platform for specifying and fitting Bayesian models. Named after Stanislaw Ulam, a pioneer of Monte Carlo methods, Stan enables researchers and practitioners to express complex statistical models in a flexible modeling language and then automatically perform full Bayesian inference using state-of-the-art algorithms.
History and Development
Stan 1.0 is released by the development team led by Andrew Gelman, Bob Carpenter, and Matt Hoffman at Columbia University, introducing Hamiltonian Monte Carlo with the No-U-Turn Sampler (NUTS) as the default inference engine.
Interfaces for R (RStan), Python (PyStan), and other languages are developed, vastly expanding Stan's user base. The Stan Math Library provides efficient automatic differentiation.
The first StanCon conference is held, bringing together users and developers from around the world.
Stan becomes a NumFOCUS sponsored project, securing long-term organizational and financial support for its development.
Stan continues to evolve with improved variational inference, within-chain parallelization, and support for GPU computation.
Technical Architecture
Stan's core is written in C++ and features a custom modeling language that supports continuous parameters, a rich library of probability distributions and mathematical functions, and automatic computation of gradients via reverse-mode automatic differentiation. The primary inference algorithm is the No-U-Turn Sampler (NUTS), an adaptive variant of Hamiltonian Monte Carlo that eliminates the need for hand-tuning step sizes and trajectory lengths. Stan also supports variational inference (ADVI), maximum a posteriori (MAP) estimation, and Laplace approximation.
Before Stan, most general-purpose Bayesian software relied on Gibbs sampling or random-walk Metropolis-Hastings algorithms, which can be painfully slow in high dimensions or with correlated parameters. Hamiltonian Monte Carlo exploits gradient information to make large, efficient moves through the posterior, dramatically improving sampling efficiency. Stan made HMC accessible to the broader statistical community for the first time.
The Development Team
Stan is developed by a distributed team of statisticians, computer scientists, and software engineers. Core contributors include Andrew Gelman, Bob Carpenter, Matt Hoffman, Michael Betancourt, Aki Vehtari, Daniel Lee, and many others. The team operates as an open-source community, with contributions welcomed from users worldwide. Governance is managed through a Stan Technical Committee that oversees the project's technical direction.
"Stan represents the democratization of Bayesian statistics. For the first time, practitioners can fit complex hierarchical models without being experts in MCMC algorithm design."— Bob Carpenter
Impact
Stan is used by thousands of researchers across academia and industry, in fields ranging from epidemiology and ecology to political science and pharmacometrics. It has been cited in thousands of peer-reviewed publications and has become the de facto standard for many applications of Bayesian statistics. The Stan ecosystem includes specialized packages such as brms (Bayesian regression models using Stan) and rstanarm (applied regression modeling), which further lower the barrier to entry.