As a surprise welcome to 2017, our paper on how the Stan language works along with an overview of how the MCMC and optimization algorithms work hit the stands this week.

• Bob Carpenter, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. 2017. Stan: A Probabilistic Programming Language. Journal of Statistical Software 76(1).

The authors are the developers at the time the first revision was submitted. We now have quite a few more developers. Because of that, we’d still prefer that people cite the manual authored by the development team collectively rather than this paper citing only some of our current developers.

The original motivation for writing a paper was that Wikipedia rejected our attempts at posting a Stan Wikipedia page without a proper citation.

I’d like to thank to Achim Zeileis at JSS for his patience and help during the final wrap up.

Abstract

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.

BibTeX

@article{stan:2017,
   author = {Bob Carpenter and Andrew Gelman and Matthew Hoffman
             and Daniel Lee and Ben Goodrich and Michael Betancourt
             and Marcus Brubaker and Jiqiang Guo and Peter Li
             and Allen Riddell},
   title = {Stan: {A} Probabilistic Programming Language},
   journal = {Journal of Statistical Software},
   volume = {76},
   number = {1},
   year = {2017}
}

Further reading

Check out the Papers about Stan section of the Stan Citations web page. There’s more info on our autodiff and on how variational inference works and a link to the original NUTS paper. And of course, don’t miss Michael’s latest if you want to understand HMC and NUTS, A conceptual introduction to HMC.