Stan is a probabilistic programming language implementing full Bayesian statistical inference with

  • MCMC sampling (NUTS, HMC),

approximate Bayesian inference with

  • Variational inference (ADVI)

and penalized maximum likelihood estimation with

  • Optimization (L-BFGS).

Stan is coded in C++ and runs on all major platforms (Linux, Mac, Windows).

Stan is freedom-respecting, open-source software (new BSD core, GPLv3 interfaces).