Because Stan is built upon a foundation of C++, contributions to the core of the project require extensive knowledge of C++ in addition to whatever statistical or algorithmic background might be needed for the given task. This includes major additions such as new algorithms or new distributions exposed to the Stan modeling language.

On the other hand, all of that C++ is hidden from the user experience by the interfaces. Consequently there are countless of ways of improving the Stan user experience without having any familiarity with C++ or professional software development. Here we mention a few possibilities for contributing to Stan without extensive C++ experience.

With the growing popularity of Bayesian inference more and more textbooks and courses are covering Bayesian methods. This is especially useful when the material focuses on a specific applied field so that the examples and exercises have direct relevance to users.

Unfortunately many such sources build their material around software packages such as BUGS which limits their utility to the Stan community. Consequently an extremely useful contribution is the translation of these course materials into Stan, first with direct translations and then with updated model implementations taking into account our current recommendations, especially for priors.

Some examples include the translation by Hiroki Ito of the ecological models introduced in "Bayesian Population Analysis using WinBUGS --- A Hierarchical Perspective" (2012) by Marc Kéry and Michael Schaub, and the translation by Martin Smira of the cognitive models introduced in “Bayesian Cognitive Modeling: A Practical Course” (2014) by Michael Lee and Eric-Jan Wagenmakers .

These translations are particularly amenable to those with domain expertise in a given field who would like to learn about Stan.

Much of our documentation, especially our case studies, is focused on a particular interface. While the interfaces are sufficiently similar that much of the content immediately translates, there are enough differences that the process can be frustrating.

Consequently an immediate contribution is translating documentation written for one interface into another, for example a case study written in RStan to one written in PyStan or CmdStan.

One of the most exciting products of the growth of Stan has been its adoption in international communities. Unfortunately that adoption can be limited by our documentation being available almost exclusively in English.

Translations of Stan documentation, including the manual and case studies, into other languages is a significant contribution towards the scalability of the entire Stan project.

A prominent example is the translation of much of the Stan documentation by the Japanese Stan community, including the translation of the RStan installation instructions by Kentaro Matsuura.

Another aspect of these efforts would be captioning the many videos that are freely available on YouTube to improve accessibility to hearing-impaired communities.

Of course you shouldn’t be limited to just translating documentation! If you have successfully applied Stan to an applied field then you are very welcome to submit a case study demonstrating that application. These case studies can be focused on introducing the Stan community to your field, your field to Bayesian inference and Stan, or both!

A Bayesian analysis isn’t complete until the fit results have been examined and reduced to interpretable products, especially visualizations. Consequently there are many contributions to be made at the interface level to improve this workflow that require only knowledge of the given environment, such as R or Python.

A recent example is BayesPlot which greatly expands the visualization facilities in RStan using ggplot2. Similar functionality in Python would be particularly welcome.

A key part of the Stan user experience is developing model specifications with Stan programs, and this development is greatly enhanced with developer tools such as program validation and syntax highlighting.

Syntax highlighting, for example, has been implemented in Atom, Emacs, and Sublime.

With the diversity of integrated development environments, however, there are many more such contributions that can be made.

Most of the Stan documentation is written by the Stan team, and we have been using Stan for so long that it becomes very easy to miss even critical steps in the documentation. For example, we may be missing important pedagogical details in the Stan manual or case studies, or subtle details in installation instructions.

Consequently a seemingly small but still important contribution to Stan is keeping track of confusing or misleading documentation or gaps in our presentations and letting us know through Discourse.

The rise of Bayesian inference has also given rise to additional software package implementing dynamic Hamiltonian Monte Carlo, like Stan, or other approximate computational algorithms. While the development team is continuously investigating new developments for inclusion into Stan, it is always helpful to have rigorous performance comparisons not only for our own understanding but also for the greater community that may not be sure which package is more useful for their problems.

Consequently we welcome carefully done performance comparisons between Stan and other software packages. These should include the model specified in both languages as well as a mathematical description and then accuracy and speed comparisons with extensively documented hardware and software environments to ensure reproducibility.

Packages like loo and bayesplot in R work with RStan, but do not have counterparts in Python to work with PyStan. Or in other interfaces.

At an even more ambitious level, there are not analogues of rstanarm or brms in Python.

Many of the contributions to the Stan language are limited not just by development challenges but also by mathematical challenges. This is particularly true for the introduction of new probability density functions.

Each density function in Stan would ideally include the analytic specification of its density, gradient, cumulative distribution function, and random number generation, each of which requires significant research before any code is written. Implementations of any of these functions that rely on expansions require particular care to ensure sufficient numerical accuracy and speed. Indeed there are many such functions in Stan that could use substantial improvements in this regard!

Documenting these functions and developing robust implementations is a contribution naturally suited to those with strong mathematical backgrounds and limited software experience. It also serves as a convenient stepping stone for subsequent development of the implementations in C++.