Stan: A Probabilistic Programming Language.

Area of Science:

• Statistical Computing
• Probabilistic Programming Languages

Background:

• Stan is a versatile probabilistic programming language designed for specifying and performing statistical inference on complex models.
• It supports a wide range of statistical modeling techniques, enabling researchers to define and analyze their models efficiently.

Purpose of the Study:

• To provide a comprehensive overview of Stan's capabilities for statistical modeling and inference.
• To highlight Stan's features for both Bayesian and frequentist approaches, including advanced computational methods.
• To detail the accessibility of computational components for custom algorithm development.

Main Methods:

• Utilizes Markov chain Monte Carlo (MCMC) methods, including the No-U-Turn sampler (NUTS), for full Bayesian inference in continuous-variable models.
• Employs optimization algorithms like the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) for penalized maximum likelihood estimation.
• Offers a platform for computing log densities, gradients, and Hessians, supporting methods like variational Bayes and expectation propagation.

Main Results:

• Stan version 2.14.0 and later provide robust Bayesian inference for continuous models.
• The language facilitates efficient calculation of penalized maximum likelihood estimates.
• Stan enables access to essential computational quantities (log densities, gradients, Hessians) for advanced inference algorithms.

Conclusions:

• Stan serves as a powerful and flexible platform for statistical modeling, offering both Bayesian and optimization-based inference.
• Its design allows for easy access to computational primitives, supporting a broad spectrum of statistical inference techniques.
• Interfaces such as CmdStan, RStan, and PyStan ensure broad usability across different computational environments.